Polynomial computations for blind image deconvolution

Abstract

This paper considers the problem of blind image deconvolution (BID) when the blur arises from a spatially invariant point spread function (PSF) H, which implies that a blurred image G is formed by the convolution of H and the exact form F of G. Since the multiplication of two bivariate polynomials is performed by convolving their coefficient matrices, the equivalence of the formation of a blurred image and the product of two bivariate polynomials implies that BID can be performed by considering F, G and H to be bivariate polynomials on which polynomial operations are performed. These operations allow the PSF to be computed, which is then deconvolved from the blurred image G, thereby obtaining a deblurred image that is a good approximation of the exact image F. Computational results show that the deblurred image obtained using polynomial computations is better than the deblurred image obtained using other methods for blind image deconvolution.