Extended Mumford-Shah Regularization in Bayesian Estimation for Blind Image Deconvolution and Segmentation

We present an extended Mumford-Shah regularization for blind image deconvolution and segmentation in the context of Bayesian estimation for blurred, noisy images or video sequences. The MumfordShah functional is extended to have cost terms for the estimation of blur kernels via a newly introduced prior solution space. This functional is minimized using Γ -convergence approximation in an embedded alternating minimization within Neumann conditions. Accurate blur identification is the basis of edge-preserving image restoration in the extended Mumford-Shah regularization. One output of the finite set of curves and object boundaries are grouped and partitioned via a graph theoretical approach for the segmentation of blurred objects. The chosen regularization parameters using the L-curve method is presented. Numerical experiments show that the proposed algorithm is efficiency and robust in that it can handle images that are formed in different environments with different types and amounts of blur and noise.