Mixture of Gaussian Blur Kernel Representation for Blind Image Restoration

Blind image restoration is a nonconvex problem involving the restoration of images using unknown blur kernels. The success of the restoration process depends on three factors: first, the amount of prior information concerning the image and blur kernel; second, the algorithm used to perform restoration; and third, the initial guesses made by the algorithm. Prior information of an image can often be used to restore the sharpness of edges. In contrast, there is no consensus concerning the use of prior information in the restoration of images from blur kernels, due to the complex nature of image blurring processes. In this paper, we model a blur kernel as a linear combination of basic two-dimensional (2-D) patterns. To illustrate this process, we constructed a dictionary comprising atoms of Gaussian functions derived from the Kronecker product of 1-D Gaussian sequences. Our results show that the proposed method is more robust than other state-of-the-art methods in a noisy environment, due to its increased signal-to-noise ratio (ISNR). This approach also proved more stable than the other methods, due to the steady increase in ISNR as the number of iterations is increased.