A non-gradient-based energy minimization approach to the image denoising problem

Abstract

A common approach to denoising images is to minimize an energy function combining a quadratic data fidelity term with a total variation-based regularization. The total variation, comprising the gradient magnitude function, originally comes from mathematical analysis and is defined on a continuous domain only. When working in a discrete domain (e.g. when dealing with digital images), the accuracy in the gradient computation is limited by the applied image resolution. In this paper we propose a new approach, where the gradient magnitude function is replaced with an operator with similar properties (i.e. it also expresses the intensity variation in a neighborhood of the considered point), but is concurrently applicable in both continuous and discrete space. This operator is the shape elongation measure, one of the shape descriptors intensively used in shape-based image processing and computer vision tasks. The experiments provided in this paper confirm the capability of the proposed approach for providing high-quality reconstructions. Based on the performance comparison of a number of test images, we can say that the new method outperforms the energy minimization-based denoising methods often used in the literature for method comparison.