Image Completion and Blind Deconvolution: Model and Algorithm

In this paper, we study a model for recovering edges in an underlying image from a single blurred image whose entries are only partially known on randomly distributed indices. In the proposed model, blurred image, the underlying image and convolution kernel are all unknowns to be solved. Besides the classical convolution-type data fitting term for image deblurring, our model incorporates nuclear norm prior for blurred image, a total variation (TV) regularization prior for recovering edges, and Tikhonov regularization prior for the blur kernel. We develop a proximal alternating minimization (PAM) iterative method to solve the model and establish its convergence. Efficient implementations are proposed for solving the subproblems arising from PAM iterations. Numerical results are reported to show the performance of our proposed approach is better than the method using TV regularization prior on the blur kernel.