Related papers: Inverse Problems with Invariant Multiscale Statist…

Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…

In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…

Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…

We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…

Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…

This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…

We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…

This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface…

Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…

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…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how…

In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…

In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…

In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to…

Imaging inverse problems aim to recover high-dimensional signals from undersampled, noisy measurements, a fundamentally ill-posed task with infinite solutions in the null-space of the sensing operator. To resolve this ambiguity, prior…