Blind image deconvolution using a robust 2-D GCD approach

Abstract

A new method is proposed for estimating an image from two of its distorted versions without the a priori knowledge of the distortion functions. In z-domain, the original image can be regarded as the greatest common polynomial divisor between the distorted versions. With the assumption that the distortion filters are FIR and relatively co-prime, this becomes a problem of taking the greatest common divisor (GCD) of two or more two-dimensional polynomials. Exact GCD is not desirable because even extremely small variations due to quantization error or additive noise will destroy the integrity of the polynomial system and lead to a trivial solution. Our method of blind image deconvolution translates the two-dimensional GCD problem into a robust one-dimensional Sylvester-type GCD algorithm. Experimental results show that it is computationally efficient and moderately noise robust.