Image deblurring - the removal of blur from an image - is one of the most important problems in image processing. Much research effort has been devoted to it, and many methods have been developed.

It is usually assumed that the degradation process that causes the blurring is not known, in which case image deblurring reduces to the problem of blind image deconvolution. In particular, the theoretically exact image is obtained by deconvolving the point spread function (PSF), which causes the blur, from the given blurred image.

It is shown in this talk that image deblurring can be performed by polynomial computations.

In this polynomial approach to image deblurring, the deblurred image (which is to be computed), the blurred image and the PSF are represented by bivariate polynomials, and thus deblurring is achieved by polynomial computations, and in particular, greatest common divisor (GCD) computations and polynomial divisions. The GCD computations are implemented by the Sylvester resultant matrix, and they allow the PSF to be calculated. The deblurred image is then obtained by deconvolving the PSF from the blurred image.

The talk will include a complete derivation of the equivalence between image deblurring and bivariate polynomial computations, and the role of the Sylvester resultant matrix for the computation of the PSF will be included. Examples of blind image deconvolution using polynomial computations will be presented, and they will include a comparison with the deblurred images obtained from other methods.