Blind Deconvolution for Symmetric Point-spread Functions

Blind deconvolution is to restore a blurred image without full information of the associated point-spread function (PSF). One recent method is to formulate an equation with only the image as unknowns by eliminating the PSF because of its symmetric property. The original image is then recovered by solving the latter equation. We present a theoretical analysis for this method in this paper. After formulating the problem in terms of the Z-transforms, it is proved that the deconvolved solutions with this method are up to a constant under additional practical assumptions on the images. We also provide a preliminary numerical experiment with a practical phantom to demonstrate the feasibility of this method.