A statistical view of iterative methods for linear inverse problems

Abstract

Ill-posed problem, Singular value decomposition, Iterative regularization methods, Model selection, Descent methods, 62F03, 62E17, 62P25,

A Threshold Regularization Method for Inverse Problems

“…In the literature of inverse problems, rates of convergence of oracles are obtained under regularity conditions on the map x 0 and the spectrum of A n . These conditions can be gathered into a single assumption, generally referred to as source condition, relating the behavior of x 0 to the regularity of the operator A n (see for instance [2], [9] or [10]). Another point of view widely adopted in the literature is the minimax approach (see [3]), aiming to determine the behavior the worst possible value of x 0 in a given class of functions.…”