An iterative variational model for blind image deconvolution

Classical image deconvolution seeks an estimate of the true image when the blur kernel or the point spread function (PSF) of the blurring system is known a priori. However, blind image deconvolution addresses the much more complicated, but realistic problem where the PSF is unknown. Bayesian inference approach with appropriate priors on the image and the blur has been used successfully to solve this blind problem, in particular with a Gaussian prior and a joint maximum a posteriori (JMAP) estimation. However, this technique is unstable and suffers from significant ringing artifacts in various applications. To overcome these limitations, we propose a regularized version using $H^1$ regularization terms on both the sharp image and the blur kernel. We present also useful techniques for estimating the smoothing parameters.  We were able to derive an efficient algorithm that produces high quality deblurred results compared to some well-known methods in the literature.