Optimal regularized image restoration algorithm based on backward diffusion equation

Abstract

Based on the interpretation of the restoration process as a backward diffusion process, an optimal filtering in terms of the spectral characteristics of an image is proposed. The restored image is given as the solution of the optimal backward diffusion equation (BDE). Several aspects of applying the backward diffusion on the blurred image are given. The ill-posedness of the backward diffusion is subdued by regularizing the speed at which the high-frequency components should be recovered by the use of a decreasing function. In manipulating the recovery speed, the spectral characteristics of an image are taken into account. The proposed scheme uses an exponentially decreasing speed function on the recovery of high-frequency components. The use of the decreasing function makes it possible to include more significant low-frequency components without failing the system, and thus yields results of better quality than the constant bounded scheme.