Accelerated iteration methods for inverse problems

Iteration methods are amongst the most common numerical tools for solving ill-posed inverse problems. Most of the computational work is needed for the evaluation of Af(m) in each iteration step. We propose to replace A by a family {B-m} of approximations, s.t. \\A-B-m\\-->0. We show 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 in order to obtain accelerated iteration schemes.