Denoising and Deblurring by Gauss Markov Random Field: An Alternating Minimization Convex Prior

In this work we propose the problem of denoising and deblurring of a degraded noisy blurred image in a single frame work. Firstly, we denoise the image containing Additive White Gaussian Noise (AWGN) and implement a non-blind deconvolution method to deblur the image using Gauss Markov random field (GMRF) prior. We estimate both the all-in-focus image and the blur sigma corresponding to the space-invariant point spread function (PSF). This problem is highly ill posed to obtain an initial estimate of blur map. We implement an MAP-GMRF alternating minimization framework to obtain the blur kernel. We calculate analytically the gradients on two direction with respect to the unknowns and show that the proposed objective function can successfully optimized with the steepest descent technique. We show results using the Gauss-Markov random field [2] prior. We show that fine details and structure information's are preserved by the GMRF regularizer. We compare the results of our algorithm with state-of-the art techniques and provide both qualitative and quantitative evaluation.