Non-local regularization of the reverse heat equation for digital images enhancement

Abstract

In 1955 Kovasznay et al. proposed to enhance an image by reversing the heat equation. This process is highly unstable and blows up the noise. Thus an efficient deblurring depends crucially on accurate denoising. In this paper we investigate the use of neighborhood filters and of a recent variant, NL-means, to stabilize the reverse heat equation. We shall prove that adding to the heat equation a term involving the self-similarities of the image stabilizes the reverse heat equation. By experiments on good quality images, not artificially blurred, we will illustrate the feasibility of the method to reveal image details. In contrast with the various PDE’s for image enhancement, the non-local reverse heat equation thus introduced is linear.