Blind image deconvolution using a robust GCD approach

In this correspondence, a new viewpoint is proposed for estimating an image from its distorted versions in presence of noise without the a priori know ledge of the distortion functions. In z-domain, the desired image can be re garded as the greatest common polynomial divisor among the distorted versio ns. With the assumption that the distortion filters are finite impulse resp onse (FIR) and relatively coprime, in the absence of noise, this becomes a problem of taking the greatest common divisor (GCD) of two or more two-dime nsional (2-D) polynomials. Exact GCD is not desirable because even extremel y small variations due to quantization error or additive noise can destroy the integrity of the polynomial system and lead to a trivial solution. Our approach to this blind deconvolution approximation problem introduces a new robust interpolative 2-D GCD method based on a one-dimensional (1-D) Sylve ster-type GCD algorithm. Experimental results with both synthetically blurr ed images and real motion-blurred pictures show that it is computationally efficient and moderately noise robust.