Jörg Polzehl

Jörg Polzehl
Weierstrass Institute for Applied Analysis and Stochastics · Stochastic Algorithms and Nonparametric Statistics

Dr. rer. nat.

About

108
Publications
11,577
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1,673
Citations

Publications

Publications (108)
Preprint
Full-text available
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...
Article
Full-text available
Younger patients increasingly receive total hip arthroplasty (THA) as therapy for end-stage osteoarthritis. To maintain the long-term success of THA in such patients, avoiding extremely high hip loads, i.e., in vivo hip contact force (HCF), is considered essential. However, in vivo HCFs are difficult to determine and their direct measurement is lim...
Book
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 p...
Chapter
Functional magnetic resonance imaging (fMRI) maps brain activity by detecting changes in image intensity related to neural activity by the blood oxygenation level-dependent (BOLD) contrast. Functional MRI data essentially consists of time series of 3D images associated with a description of the experimental conditions. The chapter outlines an analy...
Chapter
Diffusion-weighted Magnetic Resonance Imaging (dMRI) has long proven to be a versatile tool for the in vivo microstructural investigation of the human brain (Le Bihan 2003), the spinal cord (Clark et al. 1999), or even muscle tissue (Sinha et al. 2006). In contrast to conventional weighted MRI or functional MRI discussed in the preceding Chap. 4, i...
Chapter
There exist a large variety of data formats used in medical imaging in general and specifically for functional magnetic resonance imaging, diffusion-weighted imaging, or multiparameter mapping. Medical imaging data typically contain the actual data and additionally some metadata. This may be the data dimensionality, the spatial extension of the ima...
Chapter
Unlike conventional weighted MRI, leading to \(T_1\)-, \(T_2\)-, \(T_2^\star \)-, or proton density (\(P\!D\)) weighted images in arbitrary units, quantitative MRI (qMRI) aims to estimate absolute physical metrics. One example is dMRI considered in Chap. 5. qMRI is of increasing interest in neuroscience and clinical research for its greater specifi...
Chapter
Since its invention in the early 70s by Lauterbur (Lauterbur 1973; Mansfield and Grannell 1973) and Mansfield (Mansfield 1977), for which they shared the 2003 Nobel prize in Physiology and Medicine, magnetic resonance imaging (MRI) has evolved into a versatile tool for the in vivo examination of tissue. MRI is based on the nuclear magnetic resonanc...
Article
The reconstruction of geometric properties of semiconductor quantum dots (QDs) from imaging of bulk‐like samples (thickness 100‐300 nm) by transmission electron microscopy (TEM) is a difficult problem. A direct reconstruction by solving the tomography problem is not feasible due to the limited image resolution (0.5‐1 nm), the highly nonlinear behav...
Preprint
Full-text available
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...
Preprint
Full-text available
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 m...
Code
Contains R-functions to perform an fMRI analysis as described in Tabelow et al. (2006) <DOI:10.1016/j.neuroimage.2006.06.029>, Polzehl et al. (2010) <DOI:10.1016/j.neuroimage.2010.04.241>, Tabelow and Polzehl (2011) <DOI:10.18637/jss.v044.i11>.
Article
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 val...
Poster
Full-text available
In contrast to classical T1, T2, or PD-weighted imaging which acquires intensity values in arbitrary units, quantitative imaging (qMRI) has the clear advantage of providing absolute values comparable across sites and time. Multi-Parameter Mapping (MPM; Weiskopf, 2013; Lutti, 2014) is a framework for qMRI that simultaneously measures the proton dens...
Article
Full-text available
Estimation of learning curves is ubiquitously based on proportions of correct responses within moving trial windows. Thereby, 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 i...
Data
Random and systematic errors of learning curve estimation with and without accounting for session breaks. Simulations were carried out as in Fig 4. (A) Bias, (B) standard deviation (SD), (C) mean absolute error (MAE), and (D) coverage probabilities of confidence intervals of the estimated learning curves for four different window sizes (11, 19, 31,...
Data
Individual learning curves based on the constant model (conv). Learning curves (black lines) for the 20 individual rodents (R01 to R20) with 95%-confidence intervals (thin grey lines) derived from a constant model (conv) with a window of 19 trials moving across trials and session borders.—The three experimental sessions are separated by different b...
Data
Individual learning curves based on the constant model (sep). Learning curves (black lines) for the 20 individual rodents (R01 to R20) with 95%-confidence intervals (thin grey lines) derived from a constant model employed in a session-wise moving window analysis. Windows consisted of 19 trials.—The three experimental sessions are separated by diffe...
Data
Behavioral and physiological data archive. This RAR format file includes all analyzed behavioral and physiological data in ASCII format. It also contains the file Data-Documentation-001.rtf which explains the layout of the data. (RAR)
Poster
In vivo histology aims to extract biologically relevant metrics from MRI data. In neuroimaging this includes characterising white matter fibres in terms of orientation, distribution and g-ratio, or determining the cortical myelo- and cyto-architecture. It has been shown, both theoretically and experimentally, that the signal decay in gradient recal...
Article
Diffusion Kurtosis Imaging (DKI) is more sensitive to microstructural differences and can be related to more specific micro-scale metrics (e.g., intra-axonal volume fraction) than diffusion tensor imaging (DTI), offering exceptional potential for clinical diagnosis and research into the white and gray matter. Currently DKI is acquired only at low s...
Article
Full-text available
Diffusion Kurtosis Imaging (DKI) is more sensitive to microstructural differences and can be related to more specific micro-scale metrics (e.g. intra-axonal volume fraction) than diffusion tensor imaging (DTI), offering exceptional potential for clinical diagnosis and research into the white and gray matter. Currently DKI is acquired only at low sp...
Article
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 dif...
Article
Full-text available
We present a novel multi-shell position orientation adaptive smoothing (msPOAS) method for diffusion-weighted magnetic resonance data. Smoothing in voxel and diffusion gradient space is embedded in an iterative adaptive multiscale approach. The adaptive character avoids blurring of the inherent structures and preserves discontinuities. The simultan...
Poster
Full-text available
Noise in MRI effects analysis in neuroscientific problems or clinical applications. The estimation of the noise power thus serves as a measure of the quality of MRI data. On the other hand its estimates is directly used in a number of data enhancing methods to differentiate noise variation from structural differences. Most estimation methods rely o...
Article
Full-text available
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...
Article
Full-text available
SIMEX was introduced by Cook and Stefanski [6] as a simula-tion type estimator in errors-in-variables models. The idea of the SIMEX procedure is to compensate for the effect of the measure-ment errors while still using naive regression estimators. Polzehl and Zwanzig [13] defined a symmetrized version of this estima-tor. In this paper we establish...
Conference Paper
Recent studies suggest that Diffusion Kurtosis Imaging (DKI) is more sensitive to gray microstructure than the well-known diffusion tensor imaging (DTI). However, DKI suffers from a low signal-to-noise ratio (SNR), since it is based on multiple and high b-value data. Thus, in-vivo high-resolution DKI with small voxel sizes has not been available on...
Article
In this paper we develop a tensor mixture model for diffusion weighted imaging data using an automatic model order selection criterion for the number 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 investigate pro...
Article
Full-text available
We introduce an algorithm for diffusion weighted magnetic resonance imaging data enhancement based on structural adaptive smoothing in both voxel space and diffusion-gradient space. 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...
Chapter
Full-text available
Structural adaptive smoothing provides a new concept of edge-preserving non-parametric smoothing methods. In imaging it employs qualitative assumption on the underlying homogeneity structure of the image. The chapter describes the main principles of the approach and discusses applications ranging from image denoising to the analysis of functional a...
Article
Full-text available
The purpose of the package fmri is the analysis of single subject functional magnetic resonance imaging (fMRI) data. It provides fMRI analysis from time series modeling by a linear model to signal detection and publication quality images. Specifically, it implements structural adaptive smoothing methods with signal detection for adaptive noise redu...
Article
Full-text available
Diffusion weighted imaging (DWI) is a magnetic resonance (MR) based method to investigate water diffusion in tissue like the human brain. Inference focuses on integral properties of the tissue microstructure. The acquired data are usually modeled using the diffusion tensor model, a three-dimensional Gaussian model for the diffusion process. Since t...
Article
Full-text available
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 ima...
Article
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 ev...
Article
Full-text available
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) tha...
Article
Full-text available
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 clin...
Article
The paper introduces and discusses different estimation methods for multi-index models where the indices are parametric and the link function is nonparametric. We provide a new algorithm that extends the ideas of Hristache and colleagues by an additional penalization within the search space. We concentrate on an intuitive presentation of the proced...
Article
Full-text available
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 resolutio...
Article
Full-text available
The paper presents an approach to estimate parameters of a local stationary AR(1) time series model by maximization of a local likelihood function. The method is based on a propagation-separation procedure that leads to data dependent weights defining the local model. Using free propagation of weights under homogeneity, the method is capable of sep...
Article
Full-text available
An important problem of the analysis of functional magnetic resonance imaging (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, recently the propagation-separation (PS) approach has been proposed. PS is a structure adaptive smoothing method that...
Article
Full-text available
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...
Chapter
Full-text available
Regression is commonly used to describe and analyze the relation between explanatory input variables X and one or multiple responses Y. In many applications such relations are too complicated to model with a parametric regression function. Classical nonparametric regression (see e.g., Fan and Gijbels, 1996;Wand and Jones, 1995; Loader, 1999; Simono...
Chapter
Full-text available
An important problem in image and signal analysis is denoising. Given data yj at locations xj, j = 1, ..., N, in space or time, the goal is to recover the original image or signal mj, j = 1, ..., N, from the noisy observations yj, j = 1, ..., N. Denoising is a special case of a function estimation problem: If mj = m(xj) for some function m(x), we m...
Article
Full-text available
This article describes the usage of the R package fmri to analyze single time series BOLD fMRI (blood-oxygen-level dependent functional magnetic resonance imaging) data using structure adaptive smoothing procedures (Propagation- Separation approach) as described in (Tabelow et al., 2006). See (J. Polzehl and K. Tabelow, 2006) for an extended docume...
Article
Full-text available
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 sedate...
Article
Current bandwidth selectors for kernel density estimation that are asymptotically optimal often prove less promising under more moderate sample sizes. The point of this paper is to derive a class of bandwidth selectors that attain optimal root-n convergence while still showing good results under small and moderate sample sizes. This is achieved by...
Article
Full-text available
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...
Article
Full-text available
Data from functional magnetic resonance imaging (fMRI) consist of time series of brain images that are characterized by a low signal-to-noise ratio. In order to reduce noise and to improve signal detection, the fMRI data are spatially smoothed. However, the common application of a Gaussian filter does this at the cost of loss of information on spat...
Article
Full-text available
The paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models, including e.g. the regression, density, Poisson and binary response model. The method extends the adaptive weights smoothing (AWS) procedure introduced in Polzehl and Spokoiny (2000) in context of image denoising. The main idea of the met...
Technical Report
Full-text available
This document describes the usage of the R package fmri to analyse functional Magnetic Resonance Imaging (fMRI) data with structure adaptive smoothing procedures (Propagation-Separation (PS) approach) as described in [7].
Article
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 of 1994]...
Article
Full-text available
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 intr...
Article
In this paper we examine Australian data on national and regional employment numbers, focusing in particular on whether there have been common national and regional changes in the volatility of employment. A subsidiary objective is to assess whether the results derived from traditional growth rate models are sustained when alternative filtering met...
Book
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 intr...