turkmath.org

Blind image deconvolution is a very important problem in image processing because of the wide range of applications such as astronomical imaging, medical imaging, remote sensing, in which blurred images arise.It is shown that structured matrices (Bézout, Hankel, Sylvester) can be used to achieve image deblurring, more specifically by computing the approximate greatest common divisor of polynomials (GCD). We will introduce an approach witch computes the approximate GCD of two bivariate polynomials via Hankel matrices to sole the problem of blind image deconvolution. The talk will include also a fast algorithm for computing the univariate GCD of several polynomials (not pairwise) based on the generalized Bezout matrix by using Barnett's method as well as a specialized algorithm for computing the GCD of bivariate polynomials of blurred images to recover the original image.