Related papers: Controlled Total Variation regularization for inve…
This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…
We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be…
This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our…
In inverse problems, prior information and a priori-based regularization techniques play important roles. In this paper, we focus on image restoration problems, especially on restoring images whose texture mainly follow one direction. In…
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…
The conventional way of formulating inverse problems such as identification of a (possibly infinite dimensional) parameter, is via some forward operator, which is the concatenation of the observation operator with the parameter-to-state-map…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
Solving inverse problems \(Ax = y\) is central to a variety of practically important fields such as medical imaging, remote sensing, and non-destructive testing. The most successful and theoretically best-understood method is convex…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
Multidimensional continuous-domain inverse problems are often solved by the minimization of a loss functional, formed as the sum of a data fidelity and a regularization. In this work, we present a new construction where the regularization…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…
Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced performance. However, few results exist addressing the…
Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…