Blind Deblurring of Natural Stochastic Textures Using an Anisotropic Fractal Model and Phase Retrieval Algorithm

The challenging inverse problem of blind deblurring has been investigated thoroughly for natural images. Existing algorithms exploit edge-type structures, or similarity to smaller patches within the image, to estimate the correct blurring kernel. However, these methods do not perform well enough on natural stochastic textures (NSTs), which are mostly random and, in general, are not characterized by distinct edges and contours. In NST, even small kernels cause severe degradation to images. Restoration poses, therefore, an outstanding challenge. In this paper, we refine an existing method by implementing an anisotropic fractal model to estimate the blur kernel's power spectral density. The final kernel is then estimated via an adaptation of a phase retrieval algorithm, originally proposed for sparse signals. We further incorporate additional constraints that are specific to blur filters, to yield even better results. The latter are compared with results obtained by recently published blind deblurring methods.