A Separating Method for Convolution of Images Using Factorization of Polynomials

Abstract

In this paper, we show that Blind deconvolution (BD) has only finite solutions if an original image and a Point Spread Function are nonzero over a restricted domain, in other words, an observed image has finite support. Then we propose an algorithm to find all finite solutions under this boundary condition. The key of the proof is to use z-transformation and factorization of polynomials. Finally, we confirm that we can extract all sets of an original image and a PSF from a degraded image by using our algorithm in numerical examples.