Application of homotopy perturbation method to regularization of scalar images

Abstract

The homotopy perturbation method is implemented to solve nonlinear equations. Based on this method, a multi-step scheme is constructed for a kind of Hamilton-Jacobi formulations by assuming the homotopy parameter is a linear function of time. Using this multi-step scheme, a minimal surface regularization equation is solved, which designates a regularization process that doesn't smooth the image with the same weight in all the spatial directions. Some image denoisying examples illustrate its effectiveness and convenience.