A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL

In this paper,we propose a new non-local diffusion equation for noise removal,which is derived from the classical Perona-Malik equation(PM equation) and the regularized PM equation.Using the convolution of the image gradient and the gradient,we propose a new diffusion coefficient.Due to the use of the convolution,the diffusion coefficient is non-local.However,the solution of the new diffusion equation may be discontinuous and belong to the bounded variation space(BV space).By virtue of Young measure method,the existence of a BV solution to the new non-local diffusion equation is established.Experimental results illustrate that the new method has some non-local performance and performs better than the original PM and other methods.