Bayesian partial out-of-focus blur removal with parameter estimation

In this paper we propose a novel partial out-of-focus blur removal method developed within the Bayesian framework. We concentrate on the removal of background out-of-focus blurs that are present in the images in which there is a strong interest to keep the foreground in sharp focus. However, often there is a desire to recover background details out of such partially blurred image. In this work, a non-convex l_p-norm prior with 0 <; p <; 1 is used as the background and foreground image prior and a total variation (TV) based prior is utilized for both the background blur and the occlusion mask, that is, the mask determining the pixels belonging to the foreground. In order to model transparent foregrounds, the values in the occlusion mask are assumed to belong to the closed interval [0,1]. The proposed method is derived by utilizing bounds on the priors for the background and foreground image, the background blur and the occlusion mask using the majorization-minimization principle. Maximum a posteriori Bayesian inference is performed and as a result, the background and foreground image, the background blur, the occlusion mask and the model parameters are simultaneously estimated. Experimental results are presented to demonstrate the advantage of the proposed method over the existing ones.