FWT based preconditioners for Image restoration problems

The problem of removing or minimizing degradations in a blurred and noisy image is known as image restoration. The computational kernel of many image restoration problems is the solution of the following inverse problem: Hf=g+η where where the n2-vectors f and g represent the real and the observed image, respectively. The n2 vector η is an additive noise which is usually unknown. The n 2× n2-matrix H is the point spread function matrix and it represents the blurring process. The inverse problem consists in the computation of an approximation to the original image vector f, from known values of g and H. In such cases the restoration problem typically leads to a discrete ill-posed inverse problem. The classical way to compute a reasonable solution is to regularize the discrete problem. We explore the possible use of the fast wavelet transform-based preconditioners for the efficient solution of image restoration problems