Successive Over-Relaxation Technique for High-Performance Blind Image Deconvolution

This award has allowed to develop a new, mathematically sound algorithm of the blind image deconvolution, which demonstrates a superior performance when compared with existing techniques. The concept change in our approach to blind image deconvolution is in the basic strategy of addressing sensible approximate solutions to the ill-posed nonlinear inverse problem. These solutions are addresses as fixed points of the iteration which consists in alternating approximations (AA) for the object and for the PSF performed with a prescribed number of inner iterative descents from trivial (zero) initial guess. This approach shall be contrasted with traditional inexact alternating minimization (AM) approach, where a stationary point of the objective function is being targeted by the global descent trajectory, and monotonic descent to this point is terminated to achieve regularization. Artificial inversions with noise-free images show that the new approach allows the successful deconvolution of data of higher complexity, where the AM approach suffers from stagnation. In our vision, the stagnation is caused by approaching a local critical point of the cost function; these points are not necessarily the fixed points of our iteration. Inversions with real data produce solutions which are more accurate, free from the artifacts, and do not depend on the initial guess. The original document contains color images.