Related papers: An Efficient Approach for Computing Optimal Low-Ra…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
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…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…
In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…
In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…
In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a…
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…
An incoherent low-rank matrix can be efficiently reconstructed after observing a few of its entries at random, and then solving a convex program that minimizes the nuclear norm. In many applications, in addition to these entries,…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to…
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…
The numerical solution of parameter identification inverse problems for kinetic equations can exhibit high computational and memory costs. In this paper, we propose a dynamical low-rank scheme for the reconstruction of the scattering…
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…
Low-rank matrix recovery problems are inverse problems which naturally arise in various fields like signal processing, imaging and machine learning. They are non-convex and NP-hard in full generality. It is therefore a delicate problem to…
Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning…