ACCELERATED ITERATION METHODS FOR INVERSE PROBLEMS

Iteration methods are amongst the most common numerical tools for solv ing ill-posed inverse problems. Most of the computational work is need ed for the evaluation of Af(m) in each iteration step. We propose to r eplace A by a family {B-m} of approximations, s.t. \\A-B-m\\-->0. We s how that a priori or a posteriori rules for choosing B-m coupled with an adequate stopping index give rise to optimal convergence rates. The approximation B-m can be computed by wavelet-compression techniques i n order to obtain accelerated iteration schemes.