Blind Image Deconvolution: Methods and Convergence

In order to avoid the assumptions needed for convergence analysis in the Fourier domain, the authors use a general method of convergence analysis used for alternate minimization based on three point and four point properties of the points in the image space. The authors prove that all points in the image space satisfy the three point property and also derive the conditions under which four point property is satisfied. This provides the conditions under which alternate minimization for blind deconvolution converges with a quadratic prior.

Since the convergence properties depend on the chosen priors, one should design priors that avoid trivial solutions. Hence, a sparsity based solution is also provided for blind deconvolution, by using image priors having a cost that increases with the amount of blur, which is another way to prevent trivial solutions in joint estimation. This book will be a highly useful resource to the researchers and academicians in the specific area of blind deconvolution.