Related papers: Inverse Problems with Invariant Multiscale Statist…
This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a…
This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…
Scatterplots provide a visual representation of bivariate data (or 2D embeddings of multivariate data) that allows for effective analyses of data dependencies, clusters, trends, and outliers. Unfortunately, classical scatterplots suffer…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…
Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
We propose algorithms and software for computing projections onto the intersection of multiple convex and non-convex constraint sets. The software package, called SetIntersectionProjection, is intended for the regularization of inverse…
This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…
In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks.…
We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…
We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…
The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…