Second order Mumford-Shah model for image denoising

Abstract

A second order Mumford-Shah model is proposed for image denoising. Unlike the original Mumford-Shah model, the proposed new model uses second order derivatives defined in bounded Hessian space as its regulariser. This model is capable of eliminating the undesirable staircase effect associated with the original Mumford-Shah model with a total variation regulariser. Unlike other second order models that use bounded Hessian regulariser, the proposed new model does not blur the edges in the restored image. To improve computational efficiency, the implementation of the proposed model does not directly solve the high order nonlinear partial differential equations and instead exploit the efficient split Bregman algorithm, which uses the fast Fourier transform. Numerical experiments are conducted to compare the performance of the new model in image denoising with those of the original Mumford-Shah model and the pure second order model.