Polynomial computations for blind image deconvolution

This paper considers the problem of blind image deconvolution (BID) when the blur arises from a spatially invariant point spread function (PSF) HH, which implies that a blurred image GG is formed by the convolution of HH and the exact form FF of GG. 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 FF, GG and HH 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 GG, thereby obtaining a deblurred image that is a good approximation of the exact image FF. 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.