A combined total variation and bilateral filter approach for image robust super resolution

Abstract

In this paper, we consider the image super-resolution (SR) reconstitution problem. The main goal consists of obtaining a high-resolution (HR) image from a set of low-resolution (LR) ones. For that, we propose a novel approach based on a regularized criterion. The criterion is composed of the classical generalized total variation (TV) but adding a bilateral filter (BTV) regularizer. The main goal of our approach consists of the derivation and the use of an efficient combined deblurring and denoising stage that is applied on the high-resolution image. We demonstrate the existence of minimizers of the combined variational problem in the bounded variation space, and we propose a minimization algorithm. The numerical results obtained by our approach are compared with the classical robust super-resolution (RSR) algorithm and the SR with TV regularization. They confirm that the proposed combined approach allows to overcome efficiently the blurring effect while removing the noise.