Dr. Joerg Polzehl - Publications

Monografien

• J. Polzehl, K. Tabelow, Magnetic Resonance Brain Imaging: Modeling and Data Analysis using R, 2nd Revised Edition, Series: Use R!, Springer International Publishing, Cham, 2023, 258 pages, (Monograph Published), DOI 10.1007/978-3-031-38949-8 .
  Abstract
  This book discusses the modeling and analysis of magnetic resonance imaging (MRI) data acquired from the human brain. The data processing pipelines described rely on R. The book is intended for readers from two communities: Statisticians who are interested in neuroimaging and looking for an introduction to the acquired data and typical scientific problems in the field; and neuroimaging students wanting to learn about the statistical modeling and analysis of MRI data. Offering a practical introduction to the field, the book focuses on those problems in data analysis for which implementations within R are available. It also includes fully worked examples and as such serves as a tutorial on MRI analysis with R, from which the readers can derive their own data processing scripts. The book starts with a short introduction to MRI and then examines the process of reading and writing common neuroimaging data formats to and from the R session. The main chapters cover three common MR imaging modalities and their data modeling and analysis problems: functional MRI, diffusion MRI, and Multi-Parameter Mapping. The book concludes with extended appendices providing details of the non-parametric statistics used and the resources for R and MRI data.The book also addresses the issues of reproducibility and topics like data organization and description, as well as open data and open science. It relies solely on a dynamic report generation with knitr and uses neuroimaging data publicly available in data repositories. The PDF was created executing the R code in the chunks and then running LaTeX, which means that almost all figures, numbers, and results were generated while producing the PDF from the sources.

• J. Polzehl, K. Tabelow, Magnetic Resonance Brain Imaging: Modeling and Data Analysis using R, Series: Use R!, Springer International Publishing, Cham, 2019, 231 pages, (Monograph Published), DOI 10.1007/978-3-030-29184-6 .
  Abstract
  This book discusses the modeling and analysis of magnetic resonance imaging (MRI) data acquired from the human brain. The data processing pipelines described rely on R. The book is intended for readers from two communities: Statisticians who are interested in neuroimaging and looking for an introduction to the acquired data and typical scientific problems in the field; and neuroimaging students wanting to learn about the statistical modeling and analysis of MRI data. Offering a practical introduction to the field, the book focuses on those problems in data analysis for which implementations within R are available. It also includes fully worked examples and as such serves as a tutorial on MRI analysis with R, from which the readers can derive their own data processing scripts. The book starts with a short introduction to MRI and then examines the process of reading and writing common neuroimaging data formats to and from the R session. The main chapters cover three common MR imaging modalities and their data modeling and analysis problems: functional MRI, diffusion MRI, and Multi-Parameter Mapping. The book concludes with extended appendices providing details of the non-parametric statistics used and the resources for R and MRI data.The book also addresses the issues of reproducibility and topics like data organization and description, as well as open data and open science. It relies solely on a dynamic report generation with knitr and uses neuroimaging data publicly available in data repositories. The PDF was created executing the R code in the chunks and then running LaTeX, which means that almost all figures, numbers, and results were generated while producing the PDF from the sources.

• J. Polzehl, K. Tabelow, Chapter 4: Structural Adaptive Smoothing: Principles and Applications in Imaging, in: Mathematical Methods for Signal and Image Analysis and Representation, L. Florack, R. Duits, G. Jongbloed, M.-C. VAN Lieshout, L. Davies, eds., 41 of Computational Imaging and Vision, Springer, London et al., 2012, pp. 65--81, (Chapter Published).

Artikel in Referierten Journalen

• F. Galarce Marín, K. Tabelow, J. Polzehl, Ch.P. Papanikas, V. Vavourakis, L. Lilaj, I. Sack, A. Caiazzo, Displacement and pressure reconstruction from magnetic resonance elastography images: Application to an in silico brain model, SIAM Journal on Imaging Sciences, 16 (2023), pp. 996--1027, DOI 10.1137/22M149363X .
  Abstract
  This paper investigates a data assimilation approach for non-invasive quantification of intracranial pressure from partial displacement data, acquired through magnetic resonance elastography. Data assimilation is based on a parametrized-background data weak methodology, in which the state of the physical system tissue displacements and pressure fields is reconstructed from partially available data assuming an underlying poroelastic biomechanics model. For this purpose, a physics-informed manifold is built by sampling the space of parameters describing the tissue model close to their physiological ranges, to simulate the corresponding poroelastic problem, and compute a reduced basis. Displacements and pressure reconstruction is sought in a reduced space after solving a minimization problem that encompasses both the structure of the reduced-order model and the available measurements. The proposed pipeline is validated using synthetic data obtained after simulating the poroelastic mechanics on a physiological brain. The numerical experiments demonstrate that the framework can exhibit accurate joint reconstructions of both displacement and pressure fields. The methodology can be formulated for an arbitrary resolution of available displacement data from pertinent images. It can also inherently handle uncertainty on the physical parameters of the mechanical model by enlarging the physics-informed manifold accordingly. Moreover, the framework can be used to characterize, in silico, biomarkers for pathological conditions, by appropriately training the reduced-order model. A first application for the estimation of ventricular pressure as an indicator of abnormal intracranial pressure is shown in this contribution.

• S.A. Alves, J. Polzehl, N.M. Brisson, A. Bender, A.N. Agres, P. Damm, G.N. Duda, Ground reaction forces and external hip joint moments predict in vivo hip contact forces during gait, Journal of Biomechanics, 135 (2022), pp. 111037/1--111037/6, DOI 10.1016/j.jbiomech.2022.111037 .

• Y.Y. Park, J. Polzehl, S. Chatterjee, A. Brechmann, M. Fiecas, Semiparametric modeling of time-varying activation and connectivity in task-based fMRI data, Computational Statistics & Data Analysis, 150 (2020), pp. 107006/1--107006/14, DOI 10.1016/j.csda.2020.107006 .
  Abstract
  In functional magnetic resonance imaging (fMRI), there is a rise in evidence that time-varying functional connectivity, or dynamic functional connectivity (dFC), which measures changes in the synchronization of brain activity, provides additional information on brain networks not captured by time-invariant (i.e., static) functional connectivity. While there have been many developments for statistical models of dFC in resting-state fMRI, there remains a gap in the literature on how to simultaneously model both dFC and time-varying activation when the study participants are undergoing experimental tasks designed to probe at a cognitive process of interest. A method is proposed to estimate dFC between two regions of interest (ROIs) in task-based fMRI where the activation effects are also allowed to vary over time. The proposed method, called TVAAC (time-varying activation and connectivity), uses penalized splines to model both time-varying activation effects and time-varying functional connectivity and uses the bootstrap for statistical inference. Simulation studies show that TVAAC can estimate both static and time-varying activation and functional connectivity, while ignoring time-varying activation effects would lead to poor estimation of dFC. An empirical illustration is provided by applying TVAAC to analyze two subjects from an event-related fMRI learning experiment.

• J. Polzehl, K. Papafitsoros, K. Tabelow, Patch-wise adaptive weights smoothing in R, Journal of Statistical Software, 95 (2020), pp. 1--27, DOI 10.18637/jss.v095.i06 .
  Abstract
  Image reconstruction from noisy data has a long history of methodological development and is based on a variety of ideas. In this paper we introduce a new method called patch-wise adaptive smoothing, that extends the Propagation-Separation approach by using comparisons of local patches of image intensities to define local adaptive weighting schemes for an improved balance of reduced variability and bias in the reconstruction result. We present the implementation of the new method in an R package aws and demonstrate its properties on a number of examples in comparison with other state-of-the art image reconstruction methods.

• M. Deliano, K. Tabelow, R. König, J. Polzehl, Improving accuracy and temporal resolution of learning curve estimation for within- and across-session analysis, PLOS ONE, 11 (2016), pp. e0157355/1--e0157355/23, DOI 10.1371/journal.pone.0157355 .
  Abstract
  Estimation of learning curves is ubiquitously based on proportions of correct responses within moving trial windows. In this approach, it is tacitly assumed that learning performance is constant within the moving windows, which, however, is often not the case. In the present study we demonstrate that violations of this assumption lead to systematic errors in the analysis of learning curves, and we explored the dependency of these errors on window size, different statistical models, and learning phase. To reduce these errors for single subjects as well as on the population level, we propose adequate statistical methods for the estimation of learning curves and the construction of confidence intervals, trial by trial. Applied to data from a shuttle-box avoidance experiment with Mongolian gerbils, our approach revealed performance changes occurring at multiple temporal scales within and across training sessions which were otherwise obscured in the conventional analysis. The proper assessment of the behavioral dynamics of learning at a high temporal resolution clarified and extended current descriptions of the process of avoidance learning. It further disambiguated the interpretation of neurophysiological signal changes recorded during training in relation to learning.

• J. Polzehl, K. Tabelow, Low SNR in diffusion MRI models, Journal of the American Statistical Association, 111 (2016), pp. 1480--1490, DOI 10.1080/01621459.2016.1222284 .
  Abstract
  Noise is a common issue for all magnetic resonance imaging (MRI) techniques such as diffusion MRI and obviously leads to variability of the estimates in any model describing the data. Increasing spatial resolution in MR experiments further diminish the signal-to-noise ratio (SNR). However, with low SNR the expected signal deviates from the true value. Common modeling approaches therefore lead to a bias in estimated model parameters. Adjustments require an analysis of the data generating process and a characterization of the resulting distribution of the imaging data. We provide an adequate quasi-likelihood approach that employs these characteristics. We elaborate on the effects of typical data preprocessing and analyze the bias effects related to low SNR for the example of the diffusion tensor model in diffusion MRI. We then demonstrate the relevance of the problem using data from the Human Connectome Project.

• K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl, POAS4SPM --- A toolbox for SPM to denoise diffusion MRI data, Neuroinformatics, 13 (2015), pp. 19--29.
  Abstract
  We present an implementation of a recently developed noise reduction algorithm for dMRI data, called multi-shell position orientation adaptive smoothing (msPOAS), as a toolbox for SPM. The method intrinsically adapts to the structures of different size and shape in dMRI and hence avoids blurring typically observed in non-adaptive smoothing. We give examples for the usage of the toolbox and explain the determination of experiment-dependent parameters for an optimal performance of msPOAS.

• K. Tabelow, H.U. Voss, J. Polzehl, Local estimation of the noise level in MRI using structural adaptation, Medical Image Analysis, 20 (2015), pp. 76--86.
  Abstract
  We present a method for local estimation of the signal-dependent noise level in magnetic resonance images. The procedure uses a multi-scale approach to adaptively infer on local neighborhoods with similar data distribution. It exploits a maximum-likelihood estimator for the local noise level. The validity of the method was evaluated on repeated diffusion data of a phantom and simulated data using T1-data corrupted with artificial noise. Simulation results are compared with a recently proposed estimate. The method was applied to a high-resolution diffusion dataset to obtain improved diffusion model estimation results and to demonstrate its usefulness in methods for enhancing diffusion data.

• S. Mohammadi, K. Tabelow, L. Ruthotto, Th. Feiweier, J. Polzehl, N. Weiskopf, High-resolution diffusion kurtosis imaging at 3T enabled by advanced post-processing, Frontiers in Neuroscience, 8 (2015), pp. 427/1--427/14.

• S. Becker, K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl, Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS, NeuroImage, 95 (2014), pp. 90--105.
  Abstract
  In this article we present a noise reduction method (msPOAS) for multi-shell diffusion-weighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all q-shells. It is applied directly to the diffusion weighted data and consequently allows subsequent analysis by any model. Due to its adaptivity, the procedure avoids blurring of the inherent structures and preserves discontinuities. MsPOAS extends the recently developed position-orientation adaptive smoothing (POAS) procedure to multi-shell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusion-weighted data measured on a single shell and on multiple shells.

• S. Becker, K. Tabelow, H.U. Voss, A. Anwander, R.M. Heidemann, J. Polzehl, Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS), Medical Image Analysis, 16 (2012), pp. 1142--1155.
  Abstract
  We introduce an algorithm for diffusion weighted magnetic resonance imaging data enhancement based on structural adaptive smoothing in both space and diffusion direction. The method, called POAS, does not refer to a specific model for the data, like the diffusion tensor or higher order models. It works by embedding the measurement space into a space with defined metric and group operations, in this case the Lie group of three-dimensional Euclidean motion SE(3). Subsequently, pairwise comparisons of the values of the diffusion weighted signal are used for adaptation. The position-orientation adaptive smoothing preserves the edges of the observed fine and anisotropic structures. The POAS-algorithm is designed to reduce noise directly in the diffusion weighted images and consequently also to reduce bias and variability of quantities derived from the data for specific models. We evaluate the algorithm on simulated and experimental data and demonstrate that it can be used to reduce the number of applied diffusion gradients and hence acquisition time while achieving similar quality of data, or to improve the quality of data acquired in a clinically feasible scan time setting.

• K. Tabelow, H.U. Voss, J. Polzehl, Modeling the orientation distribution function by mixtures of angular central Gaussian distributions, Journal of Neuroscience Methods, 203 (2012), pp. 200--211.
  Abstract
  In this paper we develop a tensor mixture model for diffusion weighted imaging data using an automatic model selection criterion for the order of tensor components in a voxel. We show that the weighted orientation distribution function for this model can be expanded into a mixture of angular central Gaussian distributions. We show properties of this model in extensive simulations and in a high angular resolution experimental data set. The results suggest that the model may improve imaging of cerebral fiber tracts. We demonstrate how inference on canonical model parameters may give rise to new clinical applications.

• K. Tabelow, J.D. Clayden, P. Lafaye DE Micheaux, J. Polzehl, V.J. Schmid, B. Whitcher, Image analysis and statistical inference in neuroimaging with R, NeuroImage, 55 (2011), pp. 1686--1693.
  Abstract
  R is a language and environment for statistical computing and graphics. It can be considered an alternative implementation of the S language developed in the 1970s and 1980s for data analysis and graphics (Becker and Chambers, 1984; Becker et al., 1988). The R language is part of the GNU project and offers versions that compile and run on almost every major operating system currently available. We highlight several R packages built specifically for the analysis of neuroimaging data in the context of functional MRI, diffusion tensor imaging, and dynamic contrast-enhanced MRI. We review their methodology and give an overview of their capabilities for neuroimaging. In addition we summarize some of the current activities in the area of neuroimaging software development in R.

• K. Tabelow, J. Polzehl, Statistical parametric maps for functional MRI experiments in R: The package fmri, Journal of Statistical Software, 44 (2011), pp. 1--21.
  Abstract
  The package fmri is provided for analysis of single run functional Magnetic Resonance Imaging data. It implements structural adaptive smoothing methods with signal detection for adaptive noise reduction which avoids blurring of edges of activation areas. fmri provides fmri analysis from time series modeling to signal detection and publication-ready images.

• J. Polzehl, K. Tabelow, Beyond the Gaussian model in diffussion-weighted imaging: The package dti, Journal of Statistical Software, 44 (2011), pp. 1--26.
  Abstract
  Diffusion weighted imaging is a magnetic resonance based method to investigate tissue micro-structure especially in the human brain via water diffusion. Since the standard diffusion tensor model for the acquired data failes in large portion of the brain voxel more sophisticated models have bee developed. Here, we report on the package dti and how some of these models can be used with the package.

• J. Polzehl, H.U. Voss, K. Tabelow, Structural adaptive segmentation for statistical parametric mapping, NeuroImage, 52 (2010), pp. 515--523.
  Abstract
  Functional Magnetic Resonance Imaging inherently involves noisy measurements and a severe multiple test problem. Smoothing is usually used to reduce the effective number of multiple comparisons and to locally integrate the signal and hence increase the signal-to-noise ratio. Here, we provide a new structural adaptive segmentation algorithm (AS) that naturally combines the signal detection with noise reduction in one procedure. Moreover, the new method is closely related to a recently proposed structural adaptive smoothing algorithm and preserves shape and spatial extent of activation areas without blurring the borders.

• K. Tabelow, V. Piëch, J. Polzehl, H.U. Voss, High-resolution fMRI: Overcoming the signal-to-noise problem, Journal of Neuroscience Methods, 178 (2009), pp. 357--365.
  Abstract
  Increasing the spatial resolution in functional Magnetic Resonance Imaging (fMRI) inherently lowers the signal-to-noise ratio (SNR). In order to still detect functionally significant activations in high-resolution images, spatial smoothing of the data is required. However, conventional non-adaptive smoothing comes with a reduced effective resolution, foiling the benefit of the higher acquisition resolution. We show how our recently proposed structural adaptive smoothing procedure for functional MRI data can improve signal detection of high-resolution fMRI experiments regardless of the lower SNR. The procedure is evaluated on human visual and sensory-motor mapping experiments. In these applications, the higher resolution could be fully utilized and high-resolution experiments were outperforming normal resolution experiments by means of both statistical significance and information content.

• J. Polzehl, S. Sperlich, A note on structural adaptive dimension reduction, Journal of Statistical Computation and Simulation, 79 (2009), pp. 805--818.

• J. Polzehl, K. Tabelow, Structural adaptive smoothing in diffusion tensor imaging: The R package dti, Journal of Statistical Software, 31 (2009), pp. 1--24.
  Abstract
  Diffusion Weighted Imaging has become and will certainly continue to be an important tool in medical research and diagnostics. Data obtained with Diffusion Weighted Imaging are characterized by a high noise level. Thus, estimation of quantities like anisotropy indices or the main diffusion direction may be significantly compromised by noise in clinical or neuroscience applications. Here, we present a new package dti for R, which provides functions for the analysis of diffusion weighted data within the diffusion tensor model. This includes smoothing by a recently proposed structural adaptive smoothing procedure based on the Propagation-Separation approach in the context of the widely used Diffusion Tensor Model. We extend the procedure and show, how a correction for Rician bias can be incorporated. We use a heteroscedastic nonlinear regression model to estimate the diffusion tensor. The smoothing procedure naturally adapts to different structures of different size and thus avoids oversmoothing edges and fine structures. We illustrate the usage and capabilities of the package through some examples.

• K. Tabelow, J. Polzehl, A.M. Uluğ, J.P. Dyke, R. Watts, L.A. Heier, H.U. Voss, Accurate localization of brain activity in presurgical fMRI by structure adaptive smoothing, IEEE Transactions on Medical Imaging, 27 (2008), pp. 531--537.
  Abstract
  An important problem of the analysis of fMRI experiments is to achieve some noise reduction of the data without blurring the shape of the activation areas. As a novel solution to this problem, the Propagation-Separation approach (PS), a structure adaptive smoothing method, has been proposed recently. PS adapts to different shapes of activation areas by generating a spatial structure corresponding to similarities and differences between time series in adjacent locations. In this paper we demonstrate how this method results in more accurate localization of brain activity. First, it is shown in numerical simulations that PS is superior over Gaussian smoothing with respect to the accurate description of the shape of activation clusters and and results in less false detections. Second, in a study of 37 presurgical planning cases we found that PS and Gaussian smoothing often yield different results, and we present examples showing aspects of the superiority of PS as applied to presurgical planning.

• K. Tabelow, J. Polzehl, V. Spokoiny, H.U. Voss, Diffusion tensor imaging: Structural adaptive smoothing, NeuroImage, 39 (2008), pp. 1763--1773.
  Abstract
  Diffusion Tensor Imaging (DTI) data is characterized by a high noise level. Thus, estimation errors of quantities like anisotropy indices or the main diffusion direction used for fiber tracking are relatively large and may significantly confound the accuracy of DTI in clinical or neuroscience applications. Besides pulse sequence optimization, noise reduction by smoothing the data can be pursued as a complementary approach to increase the accuracy of DTI. Here, we suggest an anisotropic structural adaptive smoothing procedure, which is based on the Propagation-Separation method and preserves the structures seen in DTI and their different sizes and shapes. It is applied to artificial phantom data and a brain scan. We show that this method significantly improves the quality of the estimate of the diffusion tensor and hence enables one either to reduce the number of scans or to enhance the input for subsequent analysis such as fiber tracking.

• D. Divine, J. Polzehl, F. Godtliebsen, A propagation-separation approach to estimate the autocorrelation in a time-series, Nonlinear Processes in Geophysics, 15 (2008), pp. 591--599.

• H.U. Voss, K. Tabelow, J. Polzehl, O. Tchernichovski, K. Maul, D. Salgado-Commissariat, D. Ballon, S.A. Helekar, Functional MRI of the zebra finch brain during song stimulation suggests a lateralized response topography, Proceedings of the National Academy of Sciences of the United States of America, 104 (2007), pp. 10667--10672.
  Abstract
  Electrophysiological and activity-dependent gene expression studies of birdsong have contributed to the understanding of the neural representation of natural sounds. However, we have limited knowledge about the overall spatial topography of song representation in the avian brain. Here, we adapt the noninvasive functional MRI method in mildly sedated zebra finches (Taeniopygia guttata) to localize and characterize song driven brain activation. Based on the blood oxygenation level-dependent signal, we observed a differential topographic responsiveness to playback of bird's own song, tutor song, conspecific song, and a pure tone as a nonsong stimulus. The bird's own song caused a stronger response than the tutor song or tone in higher auditory areas. This effect was more pronounced in the medial parts of the forebrain. We found left-right hemispheric asymmetry in sensory responses to songs, with significant discrimination between stimuli observed only in the right hemisphere. This finding suggests that perceptual responses might be lateralized in zebra finches. In addition to establishing the feasibility of functional MRI in sedated songbirds, our results demonstrate spatial coding of song in the zebra finch forebrain, based on developmental familiarity and experience.

• J. Polzehl, K. Tabelow, Adaptive smoothing of digital images: The R package adimpro, Journal of Statistical Software, 19 (2007), pp. 1--17.
  Abstract
  Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used non-adaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here we present a new package adimpro for R, which implements the Propagation-Separation approach by Polzehl and Spokoiny (2006) for smoothing digital images. This method naturally adapts to different structures of different size in the image and thus avoids oversmoothing edges and fine structures. We extend the method for imaging data with spatial correlation. Furthermore we show how the estimation of the dependence between variance and mean value can be included. We illustrate the use of the package through some examples.

• J. Polzehl, K. Tabelow, fmri: A package for analyzing fmri data, Newsletter of the R Project for Statistical Computing, 7 (2007), pp. 13--17.

• K. Tabelow, J. Polzehl, H.U. Voss, V. Spokoiny, Analyzing fMRI experiments with structural adaptive smoothing procedures, NeuroImage, 33 (2006), pp. 55--62.
  Abstract
  Data from functional magnetic resonance imaging (fMRI) consists of time series of brain images which are characterized by a low signal-to-noise ratio. In order to reduce noise and to improve signal detection the fMRI data is spatially smoothed. However, the common application of a Gaussian filter does this at the cost of loss of information on spatial extent and shape of the activation area. We suggest to use the propagation-separation procedures introduced by Polzehl and Spokoiny (2006) instead. We show that this significantly improves the information on the spatial extent and shape of the activation region with similar results for the noise reduction. To complete the statistical analysis, signal detection is based on thresholds defined by random field theory. Effects of ad aptive and non-adaptive smoothing are illustrated by artificial examples and an analysis of experimental data.

• B. Röhl-Kuhn, J. Polzehl, P. Klobes, Simultaneous confidence and prediction bands in the certification of pressure-volume curves for the pore size analysis of solids by means of mercury porosimetry, Accreditation and Quality Assurance, 11 (2006), pp. 107--115.
  Abstract
  The pore size analysis of solids is widely applied in chemical industries, materials engineering, ceramic production, environmental engineering, catalysis, chromatography, nanotechnology, and many other fields. In spite of several new methods used for determining the pore size distribution of meso- and macropores [see IUPAC Recommendations, 1994] mercury porosimetry has remained one of the most popular methods employed for the characterisation of porous materials. In this paper, a new way is described for the estimation of certified pressure-volume curves from experimental curves measured by different laboratories in connection with the certification of new reference materials for a comparatively low pressure range of mercury intrusion (< 2 MPa). Simultaneous confidence and prediction bands for the certified pressure-volume curves are constructed by bootstrapping.

• J. Polzehl, V. Spokoiny, Propagation-separation approach for local likelihood estimation, Probability Theory and Related Fields, 135 (2006), pp. 335--362.
  Abstract
  The paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models, including, e.g., regression, density, Poisson and binary response models. The method extends the adaptive weights smoothing (AWS) procedure introduced by the authors [Adaptive weights smoothing with applications to image sequentation. J. R. Stat. Soc., Ser. B 62, 335-354 (2000)] in the context of image denoising. The main idea of the method is to describe a greatest possible local neighborhood of every design point in which the local parametric assumption is justified by the data. The method is especially powerful for model functions having large homogeneous regions and sharp discontinuities. The performance of the proposed procedure is illustrated by numerical examples for density estimation and classification. We also establish some remarkable theoretical non-asymptotic results on properties of the new algorithm. This includes the “propagation” property which particularly yields the root-$n$ consistency of the resulting estimate in the homogeneous case. We also state an “oracle” result which implies rate optimality of the estimate under usual smoothness conditions and a “separation” result which explains the sensitivity of the method to structural changes.

• J. Polzehl, S. Zwanzig, On a symmetrized simulation extrapolation estimator in linear errors-in-variables models, Computational Statistics & Data Analysis, 47 (2004), pp. 675-688.
  Abstract
  Application of naive regression estimates in errors-in-variables models suffers from a severe bias. The simulation extrapolation estimator (SIMEX) was introduced by Cook and Stefanski as a correction method modeling the dependence of error variance in the regressors and bias of the regression method. Our symmetrized simulation extrapolation estimator (SYMEX), a generalization of SIMEX, allows to employ the symmetric structure of errors-in-variables models. Relations of both SIMEX and SYMEX to total least squares are investigated.

• J. Polzehl, V. Spokoiny, Image denoising: Pointwise adaptive approach, The Annals of Statistics, 31 (2003), pp. 30--57.
  Abstract
  A new method of pointwise adaptation has been proposed and studied in Spokoiny (1998) in context of estimation of piecewise smooth univariate functions. The present paper extends that method to estimation of bivariate grey-scale images composed of large homogeneous regions with smooth edges and observed with noise on a gridded design. The proposed estimator $, hatf(x) ,$ at a point $, x ,$ is simply the average of observations over a window $, hatU(x) ,$ selected in a data-driven way. The theoretical properties of the procedure are studied for the case of piecewise constant images. We present a nonasymptotic bound for the accuracy of estimation at a specific grid point $, x ,$ as a function of the number of pixel $n$, of the distance from the point of estimation to the closest boundary and of smoothness properties and orientation of this boundary. It is also shown that the proposed method provides a near optimal rate of estimation near edges and inside homogeneous regions. We briefly discuss algorithmic aspects and the complexity of the procedure. The numerical examples demonstrate a reasonable performance of the method and they are in agreement with the theoretical issues. An example from satellite (SAR) imaging illustrates the applicability of the method.

• M. Hristache, A. Juditsky, J. Polzehl, V. Spokoiny, Structure adaptive approach for dimension reduction, The Annals of Statistics, 29 (2001), pp. 1537--1566.
  Abstract
  We propose a new method of effective dimension reduction for a multi-index model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension $m$ of the index space does not exceed $3$, this space can be estimated with the rate $n^-1/2$ under rather mild assumptions on the model.

• J. Polzehl, B. Grund, Semiparametric lack-of-fit tests in an additive hazard regression model, Statistics and Computing, 11 (2001), pp. 323-335.
  Abstract
  In the semiparametric additive hazard regression model of McKeague and Sasieni (Biometrika 81: 501-514), the hazard contributions of some covariates are allowed to change over time, without parametric restrictions (Aalen model), while the contributions of other covariates are assumed to be constant. In this paper, we develop tests that help to decide which of the covariate contributions indeed change over time. The remaining covariates may be modelled with constant hazard coefficients, thus reducing the number of curves that have to be estimated nonparametrically. Several bootstrap tests are proposed. The behavior of the tests is investigated in a simulation study. In a practical example, the tests consistently identify covariates with constant and with changing hazard contributions.

• J. Polzehl, V. Spokoiny, Functional and dynamic Magnetic Resonance Imaging using vector adaptive weights smoothing, Journal of the Royal Statistical Society. Series C. Applied Statistics, 50 (2001), pp. 485--501.
  Abstract
  We consider the problem of statistical inference for functional and dynamic Magnetic Resonance Imaging (MRI). A new approach is proposed which extends the adaptive weights smoothing (AWS) procedure from Polzehl and Spokoiny (2000) originally designed for image denoising. We demonstrate how the AWS method can be applied for time series of images, which typically occur in functional and dynamic MRI. It is shown how signal detection in functional MRI and analysis of dynamic MRI can benefit from spatially adaptive smoothing. The performance of the procedure is illustrated using real and simulated data.

• J. Polzehl, V. Spokoiny, Adaptive Weights Smoothing with applications to image restoration, Journal of the Royal Statistical Society. Series B. Statistical Methodology, 62 (2000), pp. 335--354.
  Abstract
  We propose a new method of nonparametric estimation which is based on locally constant smoothing with an adaptive choice of weights for every pair of data-points. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on some simulated univariate and bivariate examples and compare it with other nonparametric methods. Finally we discuss applications of this procedure to magnetic resonance and satellite imaging.

Beiträge zu Sammelwerken

• F. Galarce Marín, K. Tabelow, J. Polzehl, Ch. Panagiotis, V. Vavourakis, I. Sack, A. Caiazzo, Assimilation of magnetic resonance elastography displacement data in brain tissues, in: 7th International Conference on Computational & Mathematical Biomedical Engineering (CMBE22), 27th -- 29th June, 2022, Milan, Italy, P. Nithiarasu, C. Vergara, eds., 2, CMBE, Cardiff, UK, 2022, pp. 648--651.

• TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, On a database of simulated TEM images for In(Ga)As/GaAs quantum dots with various shapes, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices -- NUSOD 2019, J. Piprek, K. Hinze, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 13--14, DOI 10.1109/NUSOD.2019.8807025 .

• TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Towards model-based geometry reconstruction of quantum dots from TEM, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 115--116.

• K. Tabelow, J. Polzehl, SHOWCASE 21 -- Towards in-vivo histology, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 378--379.

• H. Lamecker, H.-Ch. Hege, K. Tabelow, J. Polzehl, F2 -- Image processing, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 359--376.

• J. Franke, R. Dahlhaus, J. Polzehl, V. Spokoiny, G. Steidl, J. Weickert, A. Berdychevski, S. Didas, S. Halim, P. Mrázek, S.S. Rao, J. Tadjuidje, Structural adaptive smoothing procedures, in: Mathematical Methods in Time Series Analysis and Digital Image Processing, R. Dahlhaus, J. Kurths, P. Maass, J. Timmer, eds., Understanding Complex Systems, Springer, Berlin, Heidelberg, 2008, pp. 183--229.

• J. Polzehl, V. Spokoiny, Structural adaptive smoothing by propagation-separation methods, in: Handbook of Data Visualization, caps">Ch.-h. Chen, W. Härdle, A. Unwin, eds., Springer Handbooks of Computational Statistics, Springer, Berlin, Heidelberg, 2008, pp. 471--492.

Preprints, Reports, Technical Reports

• J. Polzehl, S. Zwanzig, SIMEX and TLS: An equivalence result, Preprint no. 999, WIAS, Berlin, 2004, DOI 10.20347/WIAS.PREPRINT.999 .
  Abstract, Postscript (487 kByte), PDF (478 kByte)
  SIMEX was introduced by Cook and Stefanski (1994) as a simulation type estimator in errors-in-variables models. The idea of the SIMEX procedure is to compensate for the effect of the measurement errors while still using naive regression estimators. Polzehl and Zwanzig (2004) defined a symmetrized version of this estimator. In this paper we establish some results relating these two simulation-extrapolation-type estimators to well known consistent estimators like the total least squares estimator (TLS) and the moment estimator (MME) in the context of errors-in-variables models. We further introduce an adaptive SIMEX (ASIMEX), which is calculated like SIMEX, but based on an estimated variance. The main result of this paper is that SYMEX, ASIMEX are equivalent to TLS. Additionally we see that SIMEX is equivalent to the moment estimator.

• J. Polzehl, V. Spokoiny, Varying coefficient GARCH versus local constant volatility modeling. Comparison of the predictive power, Preprint no. 977, WIAS, Berlin, 2004, DOI 10.20347/WIAS.PREPRINT.977 .
  Abstract, Postscript (1286 kByte), PDF (606 kByte)
  GARCH models are widely used in financial econometrics. However, we show by mean of a simple simulation example that the GARCH approach may lead to a serious model misspecification if the assumption of stationarity is violated. In particular, the well known integrated GARCH effect can be explained by nonstationarity of the time series. We then introduce a more general class of GARCH models with time varying coefficients and present an adaptive procedure which can estimate the GARCH coefficients as a function of time. We also discuss a simpler semiparametric model in which the ( beta )-parameter is fixed. Finally we compare the performance of the parametric, time varying nonparametric and semiparametric GARCH(1,1) models and the locally constant model from Polzehl and Spokoiny (2002) by means of simulated and real data sets using different forecasting criteria. Our results indicate that the simple locally constant model outperforms the other models in almost all cases. The GARCH(1,1) model also demonstrates a relatively good forecasting performance as far as the short term forecasting horizon is considered. However, its application to long term forecasting seems questionable because of possible misspecification of the model parameters.

• J. Polzehl, V. Spokoiny, C. Starica, When did the 2001 recession really start?, Preprint no. 934, WIAS, Berlin, 2004, DOI 10.20347/WIAS.PREPRINT.934 .
  Abstract, Postscript (784 kByte), PDF (396 kByte)
  The paper develops a non-parametric, non-stationary framework for business-cycle dating based on an innovative statistical methodology known as Adaptive Weights Smoothing (AWS). The methodology is used both for the study of the individual macroeconomic time series relevant to the dating of the business cycle as well as for the estimation of their joint dynamic. Since the business cycle is defined as the common dynamic of some set of macroeconomic indicators, its estimation depends fundamentally on the group of series monitored. We apply our dating approach to two sets of US economic indicators including the monthly series of industrial production, nonfarm payroll employment, real income, wholesale-retail trade and gross domestic product (GDP). We find evidence of a change in the methodology of the NBER's Business-Cycle Dating Committee: an extended set of five monthly macroeconomic indicators replaced in the dating of the last recession the set of indicators emphasized by the NBER's Business-Cycle Dating Committee in recent decades. This change seems to seriously affect the continuity in the outcome of the dating of business cycle. Had the dating been done on the traditional set of indicators, the last recession would have lasted one year and a half longer. We find that, independent of the set of coincident indicators monitored, the last economic contraction began in November 2000, four months before the date of the NBER's Business-Cycle Dating Committee.

• J. Polzehl, V. Spokoiny, Varying coefficient regression modeling by adaptive weights smoothing, Preprint no. 818, WIAS, Berlin, 2003, DOI 10.20347/WIAS.PREPRINT.818 .
  Abstract, Postscript (3952 kByte), PDF (2004 kByte)
  The adaptive weights smoothing (AWS) procedure was introduced in Polzehl and Spokoiny (2000) in the context of image denoising. The procedure has some remarkable properties like preservation of edges and contrast, and (in some sense) optimal reduction of noise. The procedure is also fully adaptive and dimension free. Simulations with artificial images show that AWS is superior to classical smoothing techniques especially when the underlying image function is discontinuous and can be well approximated by a piecewise constant function. However, the latter assumption can be rather restrictive for a number of potential applications. Here the AWS method is generalized to the case of an arbitrary local linear parametric structure. We also establish some important results about properties of the AWS procedure including the so called "propagation condition" and spatial adaptivity. The performance of the procedure is illustrated by examples for local polynomial regression in univariate and bivariate situations.

• S. Mohammadi, Ch. D'alonzo, L. Ruthotto, J. Polzehl, I. Ellerbrock, M.F. Callaghan, N. Weiskopf, K. Tabelow, Simultaneous adaptive smoothing of relaxometry and quantitative magnetization transfer mapping, Preprint no. 2432, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2432 .
  Abstract, PDF (3888 kByte)
  Attempts for in-vivo histology require a high spatial resolution that comes with the price of a decreased signal-to-noise ratio. We present a novel iterative and multi-scale smoothing method for quantitative Magnetic Resonance Imaging (MRI) data that yield proton density, apparent transverse and longitudinal relaxation, and magnetization transfer maps. The method is based on the propagation-separation approach. The adaptivity of the procedure avoids the inherent bias from blurring subtle features in the calculated maps that is common for non-adaptive smoothing approaches. The characteristics of the methods were evaluated on a high-resolution data set (500 μ isotropic) from a single subject and quantified on data from a multi-subject study. The results show that the adaptive method is able to increase the signal-to-noise ratio in the calculated quantitative maps while largely avoiding the bias that is otherwise introduced by spatially blurring values across tissue borders. As a consequence, it preserves the intensity contrast between white and gray matter and the thin cortical ribbon.

• V. Avanesov, J. Polzehl, K. Tabelow, Consistency results and confidence intervals for adaptive l1-penalized estimators of the high-dimensional sparse precision matrix, Preprint no. 2229, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2229 .
  Abstract, PDF (522 kByte)
  In this paper we consider the adaptive l1-penalized estimators for the precision matrix in a finite-sample setting. We show consistency results and construct confidence intervals for the elements of the true precision matrix. Additionally, we analyze the bias of these confidence intervals. We apply the estimator to the estimation of functional connectivity networks in functional Magnetic Resonance data and elaborate the theoretical results in extensive simulation experiments.

• J. Polzehl, S. Sperlich, Structural adaptive dimension reduction, Preprint no. 1227, WIAS, Berlin, 2007, DOI 10.20347/WIAS.PREPRINT.1227 .
  Abstract, Postscript (701 kByte), PDF (294 kByte)
  The paper introduces and discusses different estimation methods for multi index models where the indices are parametric and the link function is nonparametric. More specific, the here introduced methods follow the idea of Hristache et al. (2001), modify and try to improve it. Moreover, they constitute alternatives to the so called MAVE-based methods (Xia et al, 2002). We concentrate on an intuitive presentation of what each procedure is doing to the data and its implementation. All methods considered here we have made freely available in R. We conclude with a comparative simulation study based on the provided package EDR.

• J. Polzehl, V. Spokoiny, Structural adaptive smoothing by propagation-separation methods, Preprint no. 1068, WIAS, Berlin, 2005, DOI 10.20347/WIAS.PREPRINT.1068 .
  Abstract, Postscript (66 MByte), PDF (1624 kByte)
  Propagation-Separation stands for the main properties of a new class of adaptive smoothing methods. An assumption that a prespecified type of models allows for a good local approximation within homogeneous regions in the design (structural assumption), is utilized to both recover homogeneous regions and to efficiently estimate the regression function. Locality is defined by pairwise weights. Propagation stands for the unrestricted expansion of weights within homogeneous regions. Separations characterizes the restriction of positive weights to homogeneous regions with respect to the specified model. The procedures have remarkable properties like preservation of edges and contrast, and (in some sense) optimal reduction of noise. They are fully adaptive and dimension free. We here provide a short introduction into Propagation-Separation procedures in the context of image processing. Properties are illustrated by a series of examples.

Vorträge, Poster

• A. Caiazzo, F. Galarce Marín, J. Polzehl, I. Sack, K. Tabelow, Physics based assimilation of displacements data from magnetic resonance elastography, Kick-off Workshop of the MATH+ Thematic Einstein Semester on Mathematics of Imaging in Real-World Challenges (Hybrid Event), Berlin, October 6 - 8, 2021.

• A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Model-based geometry reconstruction of quantum dots from TEM, Microscopy Conference 2019, Poster session IM 4, Berlin, September 1 - 5, 2019.

• A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Model-based geometry reconstruction of quantum dots from TEM, BMS Summer School 2019: Mathematics of Deep Learning, Berlin, August 19 - 30, 2019.

• J. Polzehl, K. Tabelow, Analyzing neuroimaging experiments within R, 2019 OHBM Annual Meeting, Organization for Human Brain Mapping, Rome, Italy, June 9 - 13, 2019.

• J. Polzehl, R Introduction, visualization and package management / Exploring functional data, Leibniz MMS Summer School 2019, October 28 - November 1, 2019, Mathematisches Forschungsinstitut Oberwolfach.

• A. Maltsi, Th. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Computing TEM images of semiconductor nanostructures, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8 - 10, 2018.

• J. Polzehl, High resolution magnetic resonance imaging experiments -- Lessons in nonlinear statistical modeling, 3rd Leibniz MMS Days, February 28 - March 2, 2018, Wissenschaftszentrum Leipzig, March 1, 2018.

• J. Polzehl, Modeling high dimensional data, Leibniz MMS Summer School 2018 on Statistical Modeling and Data Analysis, September 3 - 7, 2018, Leibniz MMS Network, Mathematisches Forschungsinstitut Oberwolfach.

• J. Polzehl, Towards in-vivo histology of the brain -- Some statistical contributions, CMRR Seminar, University of Minnesota, Center for Magnetic Resonance Research (CMRR), Minneapolis, USA, October 15, 2018.

• J. Polzehl, Connectivity networks in neuroscience -- Construction and analysis, Summer School 2017: Probabilistic and Statistical Methods for Networks, August 21 - September 1, 2017, Technische Universität Berlin, Berlin Mathematical School.

• J. Polzehl, Neue statistische Methoden zur Biomarkerselektion, Symposium ``Biomarker: Objektive Parameter als Grundlage für die erfolgreiche individuelle Therapie'', November 21, 2017, Leibniz Gesundheitstechnologien, Berlin, November 21, 2017.

• J. Polzehl, Structural adaptation -- A statistical concept for image denoising, Seminar, Isaac Newton Institute, Programme ``Variational Methods and Effective Algorithms for Imaging and Vision'', Cambridge, UK, December 5, 2017.

• J. Polzehl, Toward in-vivo histology of the brain, Neuro-Statistics: The Interface between Statistics and Neuroscience, University of Minnesota, School of Statistics (IRSA), Minneapolis, USA, May 5, 2017.

• J. Polzehl, Towards in-vivo histology of the brain, Berlin Symposium 2017: Modern Statistical Methods From Data to Knowledge, December 14 - 15, 2017, organized by Indiana Laboratory of Biostatistical Analysis of Large Data with Structure (IL-BALDS), Berlin, December 14, 2017.

• K. Tabelow, Ch. D'alonzo, L. Ruthotto, M.F. Callaghan, N. Weiskopf, J. Polzehl, S. Mohammadi, Removing the estimation bias due to the noise floor in multi-parameter maps, The International Society for Magnetic Resonance in Medicine (ISMRM) 25th Annual Meeting & Exhibition, Honolulu, USA, April 22 - 27, 2017.

• K. Tabelow, Ch. D'alonzo, J. Polzehl, Toward in-vivo histology of the brain, 2nd Leibniz MMs Days 2017, Technische Informationsbibliothek, Hannover, February 22 - 24, 2017.

• J. Polzehl, Assessing dynamics in learning experiments, Novel Statistical Methods in Neuroscience, June 22 - 24, 2016, Otto-von-Guericke-Universität Magdeburg, Institut für Mathematische Stochastik, June 22, 2016.

• J. Polzehl, Modeling high resolution MRI: Statistical issues, Mathematical and Statistical Challenges in Neuroimaging Data Analysis, January 31 - February 5, 2016, Banff International Research Station (BIRS), Banff, Canada, February 1, 2016.

• J. Polzehl, R in statistical neuroscience research, 1st Leibniz MMS Days, January 27 - 29, 2016, WIAS, January 27, 2016.

• K. Tabelow, V. Avanesov, M. Deliano, R. König, A. Brechmann, J. Polzehl, Assessing dynamics in learning experiments, Challenges in Computational Neuroscience: Transition Workshop, Research Triangle Park, North Carolina, USA, May 4 - 6, 2016.

• K. Tabelow, Ch. D'alonzo, J. Polzehl, M.F. Callaghan, L. Ruthotto, N. Weiskopf, S. Mohammadi, How to achieve very high resolution quantitative MRI at 3T?, 22th Annual Meeting of the Organization of Human Brain Mapping (OHBM 2016), Geneva, Switzerland, June 26 - 30, 2016.

• J. Polzehl, Analysing dMRI data: Consequences of low SNR, SAMSI Working group ``Structural Connectivity'', Statistical and Applied Mathematical Sciences Institute (SAMSI), Research Triangle Park, USA, December 8, 2015.

• J. Polzehl, K. Tabelow, H.U. Voss, Towards higher spatial resolution in DTI using smoothing, 21th Annual Meeting of the Organization for Human Brain Mapping, Honolulu, USA, June 14 - 18, 2015.

• J. Polzehl, K. Tabelow, Bias in low SNR diffusion MRI experiments: Problems and solution, 21th Annual Meeting of the Organization for Human Brain Mapping, Honolulu, USA, June 14 - 18, 2015.

• J. Polzehl, Noise quantification in MR experiments, Joint Statistical Meetings 2015, August 10 - 13, 2015, Seattle, USA, August 12, 2015.

• J. Polzehl, Statistical problems in diffusion weighted MR, University of Minnesota, Biostatistics-Statistics Working Group in Imaging, Minneapolis, USA, January 30, 2015.

• K. Tabelow, M. Deliano, M. Jörn, R. König, A. Brechmann, J. Polzehl, Towards a population analysis of behavioral and neural state transitions during associative learning, 21th Annual Meeting of the Organization for Human Brain Mapping, Honolulu, USA, June 14 - 18, 2015.

• S. Mohammadi, L. Ruthotto, K. Tabelow, T. Feiweier, J. Polzehl, N. Weiskopf, ACID -- A post-processing toolbox for advanced diffusion MRI, 20th Annual Meeting of the Organization for Human Brain Mapping, Hamburg, June 8 - 12, 2014.

• N. Angenstein, J. Polzehl, K. Tabelow, A. Brechmann, Categorical versus sequential processing of sound duration, 20th Annual Meeting of the Organization for Human Brain Mapping, Hamburg, June 8 - 12, 2014.

• J. Polzehl, Estimation of sparse precision matrices, MMS-Workshop ``large p small n'', WIAS-Berlin, April 15, 2014.

• J. Polzehl, Quantification of noise in MR experiments, Statistical Challenges in Neuroscience, September 3 - 5, 2014, University of Warwick, Centre for Research in Statistical Methodology, UK, September 4, 2014.

• J. Polzehl, Quantification of noise in MR experiments, International Workshop ``Advances in Optimization and Statistics'', May 15 - 16, 2014, Russian Academy of Sciences, Institute of Information Transmission Problems (Kharkevich Institute), Moscow, May 16, 2014.

• J. Polzehl, Statistical problems in diffusion weighted MR, CoSy Seminar, University of Uppsala, Department of Mathematics, Sweden, November 11, 2014.

• K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl, Adaptive noise reduction in multi-shell dMRI data with SPM by POAS4SPM, 20th Annual Meeting of the Organization for Human Brain Mapping, Hamburg, June 8 - 12, 2014.

• K. Tabelow, H.U. Voss, J. Polzehl, Local estimation of noise standard deviation in MRI images using propagation separation, 20th Annual Meeting of the Organization for Human Brain Mapping, Hamburg, June 8 - 12, 2014.

• K. Tabelow, H.U. Voss, J. Polzehl, Local estimation of the noise level in MRI images using structural adaptation, 5th Ultra-Highfield MRI Scientific Symposium, Max Delbrück Center, Berlin, June 20, 2014.

• K. Tabelow, S. Becker, S. Mohammadi, N. Weiskopf, J. Polzehl, Multi-shell position-orientation adaptive smoothing (msPOAS), 19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, USA, June 16 - 20, 2013.

• K. Tabelow, H.U. Voss, J. Polzehl, Analyzing fMRI and dMRI experiments with R, 19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, USA, June 16 - 20, 2013.

• S. Mohammadi, K. Tabelow, Th. Feiweier, J. Polzehl, N. Weiskopf, High-resolution diffusion kurtosis imaging (DKI) improves detection of gray-white matter boundaries, 19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, USA, June 16 - 20, 2013.

• J. Polzehl, Diffusion weighted magnetic resonance imaging -- Data, models and problems, Statistics Seminar, University of Minnesota, School of Statistics, USA, June 6, 2013.

• J. Polzehl, Image processing with structural adaptive smoothing, XIV. Mathematika Tag, WIAS Berlin, February 26, 2013.

• J. Polzehl, Position-orientation adaptive smoothing (POAS) in diffusion weighted imaging, Neuroimaging Data Analysis, June 9 - 14, 2013, Statistical and Applied Mathematical Sciences Institute (SAMSI), Durham (NC), USA, June 9, 2013.

• J. Polzehl, Position-orientation adaptive smoothing -- Noise reduction in dMRI, Strukturelle MR-Bildgebung in der Neuropsychiatrischen Forschung, September 13 - 14, 2013, Philipps-Universität Marburg, Klinik für Psychiatrie und Psychotherapie, Zentrum für Psychische Gesundheit, September 14, 2013.

• J. Polzehl, dMRI modeling: An intermediate step to fiber tracking and connectivity, Neuroimaging Data Analysis, June 9 - 14, 2013, Statistical and Applied Mathematical Sciences Institute (SAMSI), Durham (NC), USA, June 9, 2013.

• S. Becker, K. Tabelow, H.U. Voss, A. Anwander, R.M. Heidemann, J. Polzehl, Position-orientation adaptive smoothing (POAS) at 7T dMRI, Ultra-Highfield MRI Scientific Symposium, Max Delbrück Communication Center, Berlin, June 8, 2012.

• J. Polzehl, Adaptive methods for noise reduction in diffusion weighted MR, BRIC Seminar Series, University of North Carolina, School of Medicine, Chapel Hill, NC, USA, July 10, 2012.

• J. Polzehl, Medical image analysis in R (tutorial), The 8th International R User Conference (Use R!2012), June 11 - 15, 2012, Vanderbilt University, Department of Biostatics, Nashville, TN, USA, June 12, 2012.

• J. Polzehl, Modeling dMRI data: An introduction from a statistical viewpoint, Workshop on Neurogeometry, November 15 - 17, 2012, Masaryk University, Department of Mathematics and Statistics, Brno, Czech Republic, November 16, 2012.

• J. Polzehl, Statistical issues in diffusion weighted MR (dMRI), PreMoLab: Moscow-Berlin Stochastic and Predictive Modeling, May 31 - June 1, 2012, Russian Academy of Sciences, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, May 31, 2012.

• J. Polzehl, Statistical problems in diffusion weighted MR (dMRI), 5th International Conference of the ERCIM Working Group on Computing & Statistics (ERCIM 2012), December 1 - 3, 2012, Universidad de Oviedo, Departamento de Estadística e Investigación Operativa y Didáctica de la Matemática, Spain, December 1, 2012.

• K. Tabelow, S. Keller , S. Mohammadi, H. Kugel, J.-S. Gerdes, J. Polzehl, M. Deppe, Structural adaptive smoothing increases sensitivity of DTI to detect microstructure alterations, 17th Annual Meeting of the Organization on Human Brain Mapping (HBM 2011), Quebec City, Canada, June 26 - 30, 2011.

• K. Tabelow, H. Voss, J. Polzehl , Package dti: A framework for HARDI modeling in R, 17th Annual Meeting of the Organization on Human Brain Mapping (HBM 2011), Quebec City, Canada, June 26 - 30, 2011.

• K. Tabelow, H. Voss, J. Polzehl , Structural adaptive smoothing methods for fMRI and its implementation in R, 17th Annual Meeting of the Organization on Human Brain Mapping (HBM 2011), Quebec City, Canada, June 26 - 30, 2011.

• K. Tabelow, B. Whitcher, J. Polzehl, Performing tasks in medical imaging with R, 17th Annual Meeting of the Organization on Human Brain Mapping (HBM 2011), Quebec City, Canada, June 26 - 30, 2011.

• J. Polzehl, Statistical issues in modeling diffusion weighted magnetic resonance data, 3rd International Conference on Statistics and Probability 2011 (IMS-China), July 8 - 11, 2011, Institute of Mathematical Statistics, Xian, China, July 10, 2011.

• J. Polzehl, Modeling the orientation distribution function by mixtures of angular central Gaussian distributions, Workshop on Statistics and Neuroimaging 2011, November 23 - 25, 2011, WIAS, November 24, 2011.

• K. Tabelow, J.D. Clayden, P. Lafaye DE Micheaux, J. Polzehl, V.J. Schmid, B. Whitcher, Image analysis and statistical inference in NeuroImaging with R., Human Brain Mapping 2010, Barcelona, Spain, June 6 - 10, 2010.

• K. Tabelow, J. Polzehl, S. Mohammadi, M. Deppe, Impact of smoothing on the interpretation of FA maps, Human Brain Mapping 2010, Barcelona, Spain, June 6 - 10, 2010.

• J. Polzehl, K. Tabelow, Image and signal processing in the biomedical sciences: Diffusion-weighted imaging modeling and beyond, 1st Annual Scientific Symposium ``Ultrahigh Field Magnetic Resonance'', Max Delbrück Center, Berlin, April 16, 2010.

• J. Polzehl, Medical image analysis for structural and functional MRI, The R User Conference 2010, July 20 - 23, 2010, National Institute of Standards and Technology (NIST), Gaithersburg, USA, July 20, 2010.

• J. Polzehl, Statistical issues in accessing brain functionality and anatomy, The R User Conference 2010, July 20 - 23, 2010, National Institute of Standards and Technology (NIST), Gaithersburg, USA, July 22, 2010.

• J. Polzehl, Statistical problems in functional and diffusion weighted magnetic resonance, Uppsala University, Dept. of Mathematics, Graduate School in Mathematics and Computing, Sweden, May 27, 2010.

• J. Polzehl, Structural adaptive smoothing in neuroscience applications, Statistische Woche Nürnberg 2010, September 14 - 17, 2010, Friedrich-Alexander-Universität Erlangen-Nürnberg, Naturwissenschaftliche Fakultät, September 16, 2010.

• K. Tabelow, J. Polzehl, H.U. Voss, Structural adaptive smoothing methods for high-resolution fMRI, 15th Annual Meeting of the Organization for Human Brain Mapping (HBM 2009), San Francisco, USA, June 18 - 22, 2009.

• J. Polzehl, K. Tabelow, Structural adaptive smoothing diffusion tensor imaging data: The R-package dti, 15th Annual Meeting of the Organization for Human Brain Mapping (HBM 2009), San Francisco, USA, June 18 - 22, 2009.

• J. Polzehl, Sequential multiscale procedures for adaptive estimation, The 1st Institute of Mathematical Statistics Asia Pacific Rim Meeting, June 28 - July 1, 2009, Seoul National University, Institute of Mathematical Statistics, Korea (Republic of), July 1, 2009.

• J. Polzehl, New developments in structural adaptive smoothing: Images, fMRI and DWI, University of Tromsoe, Norway, May 27, 2008.

• J. Polzehl, Smoothing fMRI and DWI data using the propagation-separation approach, University of Utah, Computing and Scientific Imaging Institute, Salt Lake City, USA, September 11, 2008.

• J. Polzehl, Structural adaptive smoothing in diffusion tensor imaging, Workshop on ``Locally Adaptive Filters in Signal and Image Processing'', November 24 - 26, 2008, EURANDOM, Eindhoven, Netherlands, November 25, 2008.

• J. Polzehl, Structural adaptive smoothing using the propagation-separation approach, University of Chicago, Department of Statistics, USA, September 3, 2008.

• K. Tabelow, J. Polzehl, H.U. Voss, Increasing SNR in high resolution fMRI by spatially adaptive smoothing, Human Brain Mapping Conference 2007, Chicago, USA, June 10 - 14, 2007.

• K. Tabelow, J. Polzehl, H.U. Voss, Reducing the number of necessary diffusion gradients by adaptive smoothing, Human Brain Mapping Conference 2007, Chicago, USA, June 10 - 14, 2007.

• J. Polzehl, Propagation-separation procedures for image processing, International Workshop on Image Analysis in the Life Sciences, Theory and Applications, February 28 - March 2, 2007, Johannes Kepler Universität Linz, Austria, March 2, 2007.

• J. Polzehl, Structural adaptive smoothing in imaging problems, Spring Seminar Series, University of Minnesota, School of Statistics, College of Liberal Arts, USA, May 24, 2007.

• J. Polzehl, Structural adaptive smoothing methods, Gemeinsames Kolloquium des Fachbereichs Statistik und des SFB 475, Universität Dortmund, January 30, 2007.

• J. Polzehl, Structural adaptive smoothing methods and related topics, Kick-off Meeting eVITA project, Tromsø, Norway, February 15, 2007.

• J. Polzehl, Structural adaptive smoothing procedures by propagation-separation methods, Final meeting of the DFG Priority Program 1114, November 7 - 9, 2007, Freiburg, November 7, 2007.

• J. Polzehl, Structural adaptive smoothing: Images, fMRI and DWI, Workshop on Algorithms in Complex Systems, September 24 - 26, 2007, EURANDOM, Eindhoven, Netherlands, September 24, 2007.

• K. Tabelow, J. Polzehl, H.U. Voss, V. Spokoiny, Analyzing fMRI experiments with structural adaptive smoothing methods, Human Brain Mapping Conference, Florence, Italy, June 12 - 15, 2006.

• K. Tabelow, J. Polzehl, V. Spokoiny, J.P. Dyke, L.A. Heier, H.U. Voss, Accurate localization of functional brain activity using structure adaptive smoothing, ISMRM 14th Scientific Meeting & Exhibition, Seattle, USA, May 10 - 14, 2006.

• J. Polzehl, Statistische Verfahren zur Bildrekonstruktion und Signalerkennung in Bildzeitreihen, Philips GmbH, Medizintechnik, Hamburg, December 15, 2006.

• J. Polzehl, Statistische Verfahren, Bildrekonstruktion und Signalerkennung in Bildzeitreihen, Berlin, November 16, 2006.

• J. Polzehl, Structural adaptive smoothing by propagation-separation, 69th Annual Meeting of the IMS and 5th International Symposium on Probability and its Applications, July 30 - August 4, 2006, Rio de Janeiro, Brazil, July 30, 2006.

• K. Tabelow, J. Polzehl, Structure adaptive smoothing procedures in medical imaging, 19. Treffpunkt Medizintechnik ``Imaging und optische Technologien für die Medizin'', Berlin, June 1, 2005.

• J. Polzehl, Adaptive smoothing by propagation-separation, Australian National University, Center of Mathematics and its Applications, Canberra, March 31, 2005.

• J. Polzehl, Image reconstruction and edge enhancement by structural adaptive smoothing, 55th Session of the International Statistical Institute (ISI), April 5 - 12, 2005, Sydney, Australia, April 8, 2005.

• J. Polzehl, Propagation-separation at work: Main ideas and applications, National University of Singapore, Department of Probability Theory and Statistics, March 24, 2005.

• J. Polzehl, Spatially adaptive smoothing: A propagation-separation approach for imaging problems, Joint Statistical Meetings, August 7 - 11, 2005, Minneapolis, USA, August 11, 2005.

• J. Polzehl, Structural adaptive smoothing by propagation-separation methods, Ludwig-Maximilians-Universität München, SFB 386, December 7, 2005.

• J. Polzehl, Adaptive estimation for a varying coefficient GARCH model, Karlsruher Stochastik-Tage 2004, March 23 - 26, 2004, Universität Karlsruhe, March 23, 2004.

• J. Polzehl, Local likelihood modeling by structural adaptive smoothing, University of Minnesota, School of Statistics, Minneapolis, USA, September 9, 2004.

• J. Polzehl, On a nonstationary structural adaptive approach to volatility estimation, University of Gothenburg, Centre for Finance, Sweden, May 5, 2004.

• J. Polzehl, Smoothing by adaptive weights: An overview, Chalmers University of Technology, Department of Mathematical Statistics, Gothenburg, Sweden, May 11, 2004.

• J. Polzehl, Spatially adaptive smoothing: A propagation-separation approach, Workshop on New Inference Concepts for Analysing Complex Data, November 14 - 19, 2004, Mathematisches Forschungszentrum Oberwolfach, November 15, 2004.

• J. Polzehl, Structural adaptive smoothing methods, Georg-August-Universität Göttingen, Institut für Mathematische Stochastik, January 14, 2004.

• J. Polzehl, Structural adaptive smoothing methods, Tandem-Workshop on Non-linear Optimization at the Crossover of Discrete Geometry and Numerical Analysis, July 15 - 16, 2004, Technische Universität Berlin, Institut für Mathematik, July 15, 2004.

• J. Polzehl, Structural adaptive smoothing methods, 6th World Congress of the Bernoulli Society and the Institute of Mathematical Statistics, July 26 - 31, 2004, Universitat de Barcelona, Institut de Matemàtica, Spain, July 27, 2004.

• J. Polzehl, Structural adaptive smoothing methods and possible applications in imaging, Charité Berlin, NeuroImaging Center, Berlin, July 1, 2004.

• J. Polzehl, Structural adaptive smoothing methods for imaging problems, Annual Conference of Deutsche Mathematiker-Vereinigung (DMV), September 13 - 17, 2004, Heidelberg, September 14, 2004.

• J. Polzehl, Structural adaptive smoothing methods for imaging problems, German-Israeli Binational Workshop, October 20 - 22, 2004, Ollendorff Minerva Center for Vision and Image Sciences, Technion, Haifa, Israel, October 21, 2004.

• A. Hutt, J. Polzehl, Spatial adaptive signal detection in fMRT, Human Brain Mapping Conference, New York, USA, June 17 - 22, 2003.

• J. Polzehl, Adaptive smoothing procedures for image processing, Workshop on Nonlinear Analysis of Multidimensional Signals, February 25 - 28, 2003, Teistungenburg, February 25, 2003.

• J. Polzehl, Image processing using Adaptive Weights Smoothing, Uppsala University, Department of Mathematics, Sweden, May 7, 2003.

• J. Polzehl, Local likelihood modeling by Adaptive Weights Smoothing, Joint Statistical Meetings, August 3 - 7, 2003, San Francisco, USA, August 6, 2003.

• J. Polzehl, Local modeling by structural adaptation, The Art of Semiparametrics, October 19 - 21, 2003, Berlin, October 20, 2003.

• J. Polzehl, Standards needs & VAMAS role in modeling and simulation, VAMAS Steering Committee and TWA Chairmen Meeting, May 12 - 14, 2003, Petten, Netherlands, May 13, 2003.

• J. Polzehl, Structural adaptive smoothing methods and applications in imaging, Magnetic Resonance Seminar, Physikalisch-Technische Bundesanstalt, March 13, 2003.

• J. Polzehl, Statistische Grundlagen der Zertifizierung von Kurven, Bundesanstalt für Materialforschung und -prüfung, Zertifizierungskomitee der Abteilung I, Berlin, December 12, 2002.

• J. Polzehl, Structural adaptation I: Pointwise adaptive smoothing and imaging, University of Tromso, Department of Mathematics, Norway, April 11, 2002.

• J. Polzehl, Structural adaptation I: Varying coefficient regression modeling by adaptive weights smoothing, Workshop on Nonparametric Smoothing in Complex Statistical Models, April 27 - May 4, 2002, Ascona, Switzerland, April 30, 2002.

• J. Polzehl, Structural adaptation II: Time series and estimation of dimension reduction spaces, University of Tromso, Department of Mathematics, Norway, April 17, 2002.

• J. Polzehl, Structural adaptation methods in imaging, Joint Statistical Meetings 2002, August 11 - 15, 2002, New York, USA, August 12, 2002.

• J. Polzehl, Structural adaptive smoothing and its applications in imaging and time series, Uppsala University, Department of Mathematics, Sweden, May 2, 2002.

• J. Polzehl, Structural-adaptive smoothing methods, French-German Seminar, Universität Potsdam, April 6, 2002.

• J. Polzehl, Varying coefficient modeling using structural adaptation, Conference on Current Advances and Trends in Nonparametric Statistics, July 15 - 19, 2002, Crete, Greece, July 18, 2002.

• J. Polzehl, Angewandte Statistik, Continuation Seminar for Engineers, November 12 - 13, 2001, Haus der Technik, Essen.

• J. Polzehl, Can structural assumptions be used to improve nonparametric estimates?, University of Minnesota, School of Statistics, Minneapolis, USA, May 31, 2001.

• J. Polzehl, Structural adaptation in nonparametric regression, Workshop on High-Dimensional Nonlinear Statistical Modelling, September 15 - 19, 2001, Wulkow, September 16, 2001.

• J. Polzehl, Structural adaption --- A method to estimate the effective dimension reduction space, Closed Meeting of Sfb 373, May 17 - 19, 2001, Wulkow, May 18, 2001.

• J. Polzehl, Structural adaption in non-parametric smoothing, Departamento de Estadistica y Econometria, Universidad Carlos III de Madrid, Spain, March 2, 2001.

• J. Polzehl, Structural adaptive estimation, Bayer AG, Leverkusen, November 29, 2001.

• J. Polzehl, Adaptive weights smoothing and applications in imaging, Hamburger Stochastik-Tage 2000, March 21 - 24, 2000, Universität Hamburg, March 23, 2000.

• J. Polzehl, Adaptive weights smoothing with applications in imaging, Universität Essen, Fachbereich Mathematik, Sfb 475, November 6, 2000.

• J. Polzehl, Adaptive weights smoothing with applications to image denoising and signal detection, Université Catholique de Louvain-la-Neuve, Institut de Statistique, Belgium, September 29, 2000.

• J. Polzehl, Adaptive weights smoothing: What next?, Humboldt-Universität zu Berlin, Bereich Stochastik, December 19, 2000.

• J. Polzehl, Functional and dynamic Magnet Resonance Imaging using adaptive weights smoothing, Workshop "`Mathematical Methods in Brain Mapping"', Université de Montréal, Centre de Recherches Mathématiques, Canada, December 11, 2000.

• J. Polzehl, Räumlich adaptive Glättungsverfahren zur Signalerkennung in funktionellen und dynamischen MRI, Medica Research 2000, Berlin, May 11, 2000.

• J. Polzehl, Spatially adaptive procedures for signal detection in fMRI, Tagung "`Controlling Complexity for Strong Stochastic Dependencies"', September 10 - 16, 2000, Mathematisches Forschungsinstitut Oberwolfach, September 11, 2000.

• J. Polzehl, Spatially adaptive smoothing techniques for signal detection in functional and dynamic Magnet Resonance Imaging, Human Brain Mapping 2000, San Antonio, Texas, USA, June 12 - 16, 2000.

• J. Polzehl, Spatially adaptive smoothing techniques for signal detection in functional and dynamic Magnet Resonance Imaging, MEDICA 2000, Düsseldorf, November 22 - 25, 2000.

• J. Polzehl, Statistical issues in functional Magnet Resonance Imaging, Seminar Paris--Berlin, September 25 - 28, 2000, Garchy, France, September 25, 2000.

Preprints im Fremdverlag

• J.Y. Park, J. Polzehl, S. Chatterjee, A. Brechmann, ET AL., Semiparametric modeling of time-varying activation and connectivity in task-based fMRI data, Discussion paper, http://works.bepress.com/mfiecas/20, 2018.

• J. Polzehl, On a comparison of different simulation extrapolation estimators in errors-in-variables models, Preprint no. 17, Uppsala University, Department of Mathematics, 2003.