相关论文: Parallel proximal methods for total variation mini…
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…
We study the problem of recovering piecewise-polynomial periodic functions from their low-frequency information. This means that we only have access to possibly corrupted versions of the Fourier samples of the ground truth up to a maximum…
This article studies the denoising performance of total variation (TV) image regularization. More precisely, we study geometrical properties of the solution to the so-called Rudin-Osher-Fatemi total variation denoising method. The first…
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…
While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or…
The problem of minimization of the sum of two convex functions has various theoretical and real-world applications. One of the popular methods for solving this problem is the proximal gradient method (proximal forward-backward algorithm). A…
Flash X-ray computed tomography (CT) is an important imaging modality for characterization of high-speed dynamic events, such as Kolsky bar impact experiments for the study of mechanical properties of materials subjected to impulsive…
Invariant risk minimization is an important general machine learning framework that has recently been interpreted as a total variation model (IRM-TV). However, how to improve out-of-distribution (OOD) generalization in the IRM-TV setting…
We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general…
In this paper we investigate the problem of recovering the source term in an elliptic system from a measurement of the state on a part of the boundary. For the particular interest in reconstructing probably discontinuous sources, we use the…
In the past decade, sparsity-driven regularization has led to significant improvements in image reconstruction. Traditional regularizers, such as total variation (TV), rely on analytical models of sparsity. However, increasingly the field…
This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such problems we consider regularizers consisting of two terms that must be…
Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically…
Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for…
The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images, such as sharp edges and enables spectral, scale, and texture analysis.…
A fundamental concept in solving inverse problems is the use of regularizers, which yield more physical and less-oscillatory solutions. Total variation (TV) has been widely used as an edge-preserving regularizer. However, objects are often…
This paper presents a sparse Bayesian learning algorithm for inverse problems in signal and image processing with a total variation (TV) sparsity prior. Because of the prior used, and the fact that the prior parameters are estimated…
This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It…
In this article, we offer a novel numerical approach for the solution of elastohydrodynamic lubrication line and point contact problems using a class of total variation diminishing (TVD) schemes on parallel computers. A direct parallel…
We propose an efficient estimation technique for the automatic selection of locally-adaptive Total Variation regularisation parameters based on an hybrid strategy which combines a local maximum-likelihood approach estimating space-variant…