A multiresolution model of iterative regularized image restoration

Abstract

A model of iterative regularized restoration of images based upon wavelet filter banks is proposed in this paper. Regularized restoration is a method of solving ill-posed image restoration problems. Wavelet filter-banks designed upon arbitrarily sampling lattices are proposed in order to replace the conventional regularization operator. A regularization parameter corresponds to each decomposition channel of the wavelet filter-bank. The proposed model estimates regularization parameters iteratively. The current estimate of the restored image is used in such an estimation. The model assumes that the degradation may be represented by a perfect reconstruction filter bank. Factorizations of unitary matrices using Givens rotations allow for efficient representations of a variety of degradations. Should both the degradation and the smoothing filter be decomposed by wavelet filter banks, the restoration problem may be split into independent restoration problems in each transformation channel. Regularization parameters are evaluated iteratively in each channel. Numerical results indicate better (improvement in signal-to-noise-ratio) figures conventional iterative regularization methods.