Improved ADMM based TV minimized Image deblurring without boundary artifacts

Edge preserving (e.g. total variation minimized) regularized image deblurring methods are actively researched with many practical applications. Formally this type of deblurring is equivalent to a convex non-smooth optimization problem. In this paper we describe an ADMM optimization based effective algorithm, which can be considered as an improved version of a previously published method. Due to the introduced modifications different loss functions can be easily used, positivity constraint is applied and the speed of the convergence of deblurring is also increased. The quality of the deblurring in the cases of using different loss functions is compared qualitatively and quantitatively and the accelerating rate of the convergence is also examined. For these measurements benchmark images were used. Based on our experiments we suggest to consider Huber function as loss function instead of the commonly used quadratic functions.