Related papers: On a Constrained Pseudoinverse for the Electromagn…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
We consider two phaseless inverse problems for elliptic equation. The statements of these problems differ from have considered. Namely, instead of given information about modulus of scattering waves, we consider the information related to…
We consider solving ill-posed imaging inverse problems without access to an explicit image prior or ground-truth examples. An overarching challenge in inverse problems is that there are many undesired images that fit to the observed…
The well-known M-P (Moore-Penrose) pseudoinverse is used in several linear-algebra applications; for example, to compute least-squares solutions of inconsistent systems of linear equations. Irrespective of whether a given matrix is sparse,…
Signal restoration and inverse problems are key elements in most real-world data science applications. In the past decades, with the emergence of machine learning methods, inversion of measurements has become a popular step in almost all…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
This paper investigates the comparative performance of two fundamental approaches to solving linear regression problems: the closed-form Moore-Penrose pseudoinverse and the iterative gradient descent method. Linear regression is a…
Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a…
The aim of this work is to characterize linear maps of inner pro\-duct infinite-dimensional vector spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in…
Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…
The inverse source problem in electromagnetics has proved quite relevant for a large class of applications. In antenna diagnostics in particular, Love solutions are often sought at the cost of an increase of the dimension of the linear…
This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a…
Inverse modeling for computing a high-dimensional spatially-varying property field from indirect sparse and noisy observations is a challenging problem. This is due to the complex physical system of interest often expressed in the form of…
We introduce PseudoNet, a new pseudolikelihood-based estimator of the inverse covariance matrix, that has a number of useful statistical and computational properties. We show, through detailed experiments with synthetic and also real-world…
In this paper, firstly we study the continuity of the core-EP inverse without explicit error bounds by virtue of two methods. One is the rank equality, followed from the classical generalized inverse. The other one is matrix decomposition.…
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…