Sparse Representation of a Blur Kernel for Blind Image Restoration

Abstract: Blind image restoration is a non-convex problem which involves restoration of images from an unknown blur kernel. The factors affecting the performance of this restoration are how much prior information about an image and a blur kernel are provided and what algorithm is used to perform the restoration task. Prior information on images is often employed to restore the sharpness of the edges of an image. By contrast, no consensus is still present regarding what prior information to use in restoring from a blur kernel due to complex image blurring processes. In this paper, we propose modelling of a blur kernel as a sparse linear combinations of basic 2-D patterns. Our approach has a competitive edge over the existing blur kernel modelling methods because our method has the flexibility to customize the dictionary design, which makes it well-adaptive to a variety of applications. As a demonstration, we construct a dictionary formed by basic patterns derived from the Kronecker product of Gaussian sequences. We also compare our results with those derived by other state-of-the-art methods, in terms of peak signal to noise ratio (PSNR).