Related papers: Adaptive Regularization of Ill-Posed Problems: App…
We propose an automated nonlinear model reduction and mesh adaptation framework for rapid and reliable solution of parameterized advection-dominated problems, with emphasis on compressible flows. The key features of our approach are…
Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance…
Classical pairwise image registration methods search for a spatial transformation that optimises a numerical measure that indicates how well a pair of moving and fixed images are aligned. Current learning-based registration methods have…
Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…
In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…
Graphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of…
Rigid slice-to-volume registration is a challenging task, which finds application in medical imaging problems like image fusion for image guided surgeries and motion correction for volume reconstruction. It is usually formulated as an…
Gaussian Markov random fields (GMRFs) are popular for modeling dependence in large areal datasets due to their ease of interpretation and computational convenience afforded by the sparse precision matrices needed for random variable…
Data augmentation has been proven to be an effective technique for developing machine learning models that are robust to known classes of distributional shifts (e.g., rotations of images), and alignment regularization is a technique often…
This paper presents two new augmented flexible (AF)-Krylov subspace methods, AF-GMRES and AF-LSQR, to compute solutions of large-scale linear discrete ill-posed problems that can be modeled as the sum of two independent random variables,…
Image registration is a key technique in medical image analysis to estimate deformations between image pairs. A good deformation model is important for high-quality estimates. However, most existing approaches use ad-hoc deformation models…
We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve…
We present deformable unsupervised medical image registration using a randomly-initialized deep convolutional neural network (CNN) as regularization prior. Conventional registration methods predict a transformation by minimizing…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…
In this work we consider the problem of finding optimal regularization parameters for general-form Tikhonov regularization using training data. We formulate the general-form Tikhonov solution as a spectral filtered solution using the…
Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…
We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data. We use the Wasserstein-2 geometry to capture semantically meaningful neighborhoods in the space of images, and…
In this paper, we present a short description of the method proposed to ANHIR challenge organized jointly with the IEEE ISBI 2019 conference. We propose a method consisting of preprocessing, initial alignment, nonrigid registration…
In this paper we investigate adaptive discretization of the iteratively regularized Gauss- Newton method IRGNM. All-at-once formulations considering the PDE and the measurement equation simultaneously allow to avoid (approximate) solution…