The thesis addresses two important nonlinear inverse problems in image processing: the separation of show-through and the bleed-trough mixtures and the blind deblurring of images. New solutions to cope with their high levels of indetermination are proposed.

Two separation methods are developed for the first problem. In a first approach, the indeterminacy of nonlinear Independent Component Analysis (ICA) is reduced through the use of a physical model with only four parameters. Based on other properties, a wavelet-based method is also developed. This non-iterative approach performs space-variant non pixel-wise separation.

Both techniques reach separation results competitive with those of other methods.

Regarding blind deblurring, the technique that is developed does not impose strong restrictions on the blurring filter, overcoming the ill-posedness of Blind Image Deconvolution (BID) by initially considering the main image edges and, progressively, handling fainter and smaller ones.

The BID technique is extended for deblurring shift-variant degradations in which the blurred image consists of two layers that were subjected to different degradations. The approach is successfully tested on several images, with a variety of synthetic and real-life blurs, both in shift-invariant and two-layer problems. The deblurring results are visually and quantitatively better than those obtained with other state-of-the-art methods.