A generalized Landweber iteration for ill-conditioned signal restoration

The authors examine a generalized version of Landweber´s iteration using spectral filter analysis, which leads them to propose a modification of the iteration to improve its performance in solving ill-conditioned linear systems. The regularization concept is incorporated into the generalized version of Landweber´s iteration. Two functions for determining critical parameter values are examined: a generalized cross-validation function and an estimate of the mean-square error between the true and computed solutions. The performance of the proposed method is demonstrated by presenting a signal restoration example