Two-Dimensional Blind Deconvolution Using a Robust GCD Approach

S. Unnikrishna Pillai, Ben Liang

Abstract: We examine the applicability of the previously proposed greatest common divisor (GCD) method to blind image deconvolution. In this method, the desired image is approximated as the GCD of the two-dimensional polynomials corresponding to the z-transforms of two or more distorted and noisy versions of the same scene, assuming that the distortion filters are FIR and relatively co-prime. We justify the breakdown of two-dimensional GCD into one-dimensional Sylvester-type GCD algorithms, which lowers the computational complexity while maintaining the noise robustness. A way of determining the support size of the true image is also described. We also provide a solution to deblurring using the GCD method when only one blurred image is available. Experimental results are shown using both synthetically blurred images and real motion-blurred pictures.