Nonconvex Bayesian Restoration of Blurred Foreground Images

Recently, some techniques for deblurring images having arbitrarily shaped boundaries have been proposed. However, when we observe a blurry foreground (FG) object on a sharp background (BG) there is no abrupt transition between them. Because previous techniques are not designed to cop with a smooth transition area between FG and BG, they avoid it by artificially discarding it from the computations. Here we construct, instead, an observation model that accounts for the occlusion photometric effect of the FG object on the BG, and we illustrate its realism by comparing a simulation with a real capture. Then we use that observation model to pose a Bayesian MAP estimation problem with an L2-relaxed L0 sparse prior and two Gaussian likelihood terms (for the noise, and for the BG interference in the smooth transition area), which we solve by alternating optimizations. Using simulations, we demonstrate a higher performance of our method, compared to two state-of-the-art unconstrained boundary restoration techniques.