Blind deconvolution of images with model discrepancies using maximum a posteriori estimation with heavy-tailed priors

Single image blind deconvolution aims to estimate the unknown blur from a single observed blurred image and recover the original sharp image. Such task is severely ill-posed and typical approaches involve some heuristic or other steps without clear mathematical explanation to arrive at an acceptable solution. We show that a straightforward maximum a posteriori estimation incorporating sparse priors and mechanism to deal with boundary artifacts, combined with an efficient numerical method can produce results which compete with or outperform much more complicated state-of-the-art methods. Our method is naturally extended to deal with overexposure in low-light photography, where linear blurring model is violated.