As the traditional fourth order partial differential equation(fourth order equation)algorithm causes edge leakage of image

a leakage compensation method is proposed based on edge detection theory.Firstly the noise image is preprocessed by a nonlinear bilateral filter to obtain the better edge preservation image.Based on the feature of the gradient operator on the detection of image edge and the squared two-norm of gradient difference which is between the result image and the preprocessed image

a constraint item is built.Then the constraint item is added to the corresponding energy functional of fourth order equation.Finally

to adaptively adjust the edge preservation constraint item and improve the performance of edge preservation

an adaptive Lagrange multiplier which is based on image local variance is constructed.The experimental results show that the proposed algorithm not only inherits the advantage of traditional fourth order equation

but also enhances its ability of edge preservation.