Iterative Inversion Methods for Statistical Inverse Problems

Inverse Problems in Imaging Systems and the General Bayesian Inversion Frawework

In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Baye...

A stable iteration to the matrix inversion

The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Preconditioned iterative methods for linear discrete ill-posed problems from a Bayesian inversion perspective

In this paper we revisit the solution of ill-posed problems by preconditioned iterative methods from a Bayesian statistical inversion perspective. After a brief review of the most popular Krylov subspace iterative methods for the solution of linear discrete illposed problems and some basic statistics results, we analyze the statistical meaning of left and right preconditioners, as well as proje...

Dynamic level set regularization for large distributed parameter estimation problems

This article considers inverse problems of shape recovery from noisy boundary data, where the forward problem involves the inversion of elliptic PDEs. The piecewise constant solution, a scaling and translation of a characteristic function, is described in terms of a smoother level set function. A fast and simple dynamic regularization method has been recently proposed that has a robust stopping...