Blind image deconvolution using the Sylvester resultant matrix

This paper uses techniques from computational algebraic geometry to perform blind image deconvolution, such that prior knowledge of the point spread function (PSF) is not required to compute a deblurred form of a given blurred image. In particular, it is shown that the Sylvester resultant matrix enables the PSF to be calculated by two approximate greatest common divisor computations. These computations, and not greatest common divisor computations, are required because of the noise that is present in the exact image and PSF. The computed PSF is then deconvolved from the blurred image in order to calculate the deblurred image. The experimental results show consistently good results for the deblurred image and PSF, and they are compared with the results from other methods for blind image deconvolution.