Blind deconvolution of images and small-extent point-spread functions using resultant matrices

The 2-D blind deconvolution problem is to reconstruct an image having known finite spatial extent from its 2-D convolution with an also-unknown point-spread function. This is significantly more difficult than the typical image restoration problem of deconvolving a known blurring function. Many methods for solving this problem are iterative but not POCS, and they tend to stagnate. We present a completely novel approach that assumes the unknown point-spread function varies slowly in the 2-D Z-transform domain, as would be the case if the point-spread function had small spatial extent. Sampling the problem along one axis in the 2-D Z-transform domain, and assuming the image transform varies between samples while the point-spread function transform does not, results in an approximate polynomial greatest common divisor problem. This can be solved by finding the eigenvector associated with the minimum eigenvalue of a resultant matrix. Repeating for several samples allows the point-spread function to be reconstructed using Lagrange interpolation