Related papers: Total Deep Variation: A Stable Regularizer for Inv…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
Data-driven approaches recently achieved remarkable success in magnetic resonance imaging (MRI) reconstruction, but integration into clinical routine remains challenging due to a lack of generalizability and interpretability. In this paper,…
In the past, optimization-based registration models have used spatially-varying regularization to account for deformation variations in different image regions. However, deep learning-based registration models have mostly relied on…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
Objective: This paper investigates how generative models, trained on ground-truth images, can be used \changes{as} priors for inverse problems, penalizing reconstructions far from images the generator can produce. The aim is that learned…
In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…
Recently, a large number of efficient deep learning methods for solving inverse problems have been developed and show outstanding numerical performance. For these deep learning methods, however, a solid theoretical foundation in the form of…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii)…
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is…
Magnetic Resonance Imaging can produce detailed images of the anatomy and physiology of the human body that can assist doctors in diagnosing and treating pathologies such as tumours. However, MRI suffers from very long acquisition times…
We propose a new type of regularization functional for images called oscillation total generalized variation (TGV) which can represent structured textures with oscillatory character in a specified direction and scale. The infimal…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
Learning neural networks using only few available information is an important ongoing research topic with tremendous potential for applications. In this paper, we introduce a powerful regularizer for the variational modeling of inverse…
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…
The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…
The solution of inverse problems is crucial in various fields such as medicine, biology, and engineering, where one seeks to find a solution from noisy observations. These problems often exhibit non-uniqueness and ill-posedness, resulting…
This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…
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…
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…