Efficient Blind Separable Kernel Deconvolution for Image Deblurring

Abstract

This paper develops a novel, efficient, 2D, blind deconvolution algorithm for restoring images corrupted by an unknown 2D blurring kernel satisfying a separable property. The algorithm builds on known results for 2D deconvolution using the Constant Modulus Algorithm (CMA) which is an archetype gradient descent based blind algorithm used in 1D blind deconvolution of communication systems. By exploiting the separable property of kernels there is a substantial speedup relative to an unstructured 2D blurring kernel. That is, for a 2N +1× 2N +1 kernel the complexity is improved by a factor of O(N), the reduction in parameters greatly improves speed of convergence, robustness and accuracy of the deconvolution. The algorithm and a class of generalizations are derived, and the performance improvement claims are corroborated through a set of simulations.