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- ItemPatch-Wise Adaptive Weights Smoothing in R(Los Angeles, Calif. : UCLA, Dept. of Statistics, 2020) Polzehl, Jörg; Papafitsoros, Kostas; Tabelow, KarstenImage 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. © 2020, American Statistical Association. All rights reserved.
- ItemMathematical models as research data via flexiformal theory graphs(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Kohlhase, Michael; Koprucki, Thomas; Müller, Dennis; Tabelow, KarstenMathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extent the corresponding scientific software as research data. But both have their origin in mathematical models, therefore any holistic approach to research data in MMS should cover all three aspects: data, software, and models. While the problems of classifying, archiving and making accessible are largely solved for data and first frameworks and systems are emerging for software, the question of how to deal with mathematical models is completely open. In this paper we propose a solution to cover all aspects of mathematical models: the underlying mathematical knowledge, the equations, boundary conditions, numeric approximations, and documents in a flexiformal framework, which has enough structure to support the various uses of models in scientific and technology workflows. Concretely we propose to use the OMDoc/MMT framework to formalize mathematical models and show the adequacy of this approach by modeling a simple, but non-trivial model: van Roosbroecks drift-diffusion model for one-dimensional devices. This formalization and future extensions allows us to support the modeler by e.g. flexibly composing models, visualizing Model Pathway Diagrams, and annotating model equations in documents as induced from the formalized documents by flattening. This directly solves some of the problems in treating MMS as research data and opens the way towards more MKM services for models.
- ItemStructural adaptive segmentation for statistical parametric mapping(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Polzehl, Jörg; Voss, Henning U.; Tabelow, KarstenFunctional 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.
- ItemStructural adaptive smoothing: principles and applications in imaging(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Polzehl, Jörg; Tabelow, KarstenStructural 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 and diffusion weighted Magnetic Resonance experiments.
- ItemLocal estimation of the noise level in MRI using structural adaptation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Tabelow, Karsten; Voss, Henning U.; Polzehl, JörgWe 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.
- ItemBeyond the diffusion tensor model: the package dti(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Polzehl, Jörg; Tabelow, KarstenDiffusion 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.
- ItemDiffusion tensor imaging : structural adaptive smoothing(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Tabelow, Karsten; Polzehl, Jörg; Spokoiny, Vladimir; Voss, Henning U.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.
- ItemDisplacement and pressure reconstruction from magnetic resonance elastography images: Application to an in silico brain model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Galarce Marín, Felipe; Tabelow, Karsten; Polzehl, Jörg; Papanikas, Christos Panagiotis; Vavourakis, Vasileios; Lilaj, Ledia; Sack, Ingolf; Caiazzo, AlfonsoThis 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.
- ItemImage analysis and statistical inference in neuroimaging with R(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Tabelow, Karsten; Clayden, Jon D.; Lafaye de Micheaux, Pierre; Polzehl, Jörg; Schmid, Volker J.; Whitcher, BrandonR 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.
- ItemMore specific signal detection in functional magnetic resonance imaging by false discovery rate control for hierarchically structured systems of hypotheses(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Schildknecht, Konstantin; Tabelow, Karsten; Dickhaus, ThorstenSignal detection in functional magnetic resonance imaging (fMRI) inherently involves the problem of testing a large number of hypotheses. A popular strategy to address this multiplicity is the control of the false discovery rate (FDR). In this work we consider the case where prior knowledge is available to partition the set of all hypotheses into disjoint subsets or families, e. g., by a-priori knowledge on the functionality of certain regions of interest. If the proportion of true null hypotheses differs between families, this structural information can be used to increase statistical power. We propose a two-stage multiple test procedure which first excludes those families from the analysis for which there is no strong evidence for containing true alternatives. We show control of the family-wise error rate at this first stage of testing. Then, at the second stage, we proceed to test the hypotheses within each non-excluded family and obtain asymptotic control of the FDR within each family in this second stage. Our main mathematical result is that this two-stage strategy implies asymptotic control of the FDR with respect to all hypotheses. In simulations we demonstrate the increased power of this new procedure in comparison with established procedures in situations with highly unbalanced families. Finally, we apply the proposed method to simulated and to real fMRI data.