Related papers: Analysis of regularization methods for the solutio…

We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…

We introduce a notion of tractability for ill-posed operator equations in Hilbert space. For such operator equations the asymptotics of the best possible rate of reconstruction in terms of the underlying noise level is known in many cases.…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation…

In this paper, we consider the asymptotical regularization with convex constraints for nonlinear ill-posed problems. The method allows to use non-smooth penalty terms, including the L1-like and the total variation-like penalty functionals,…

Most of the literature on the solution of linear ill-posed operator equations, or their discretization, focuses only on the infinite-dimensional setting or only on the solution of the algebraic linear system of equations obtained by…

We describe a method to discretize optimization problems arising in the regularization of linear inverse problem having compact forward operator defined on 3-D valed measures, compactly supported on a fixed set. The criterion is a quadratic…

For approximately solving linear ill-posed problems in Hilbert spaces, we investigate the regularization properties of the aggregation method and the RatCG method. These recent algorithms use previously calculated solutions of Tikhonov…

An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with…

In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…

Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…

In recent years, new regularization methods based on (deep) neural networks have shown very promising empirical performance for the numerical solution of ill-posed problems, e.g., in medical imaging and imaging science. Due to the…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…

In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace…

In this paper, we propose a level set regularization approach combined with a split strategy for the simultaneous identification of piecewise constant diffusion and absorption coefficients from a finite set of optical tomography data…

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…

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a…

We propose a regularization method to solve a nonlinear ill-posed problem connected to inversion of data gathered by a ground conductivity meter.