Study On PDE-Based Image Restoration Methods

PDE-based image restoration methods were divided two kinds: axiomatic approach and variational Approach. In our study, three common frameworks in the two kinds of methods were modified and then diffusion coefficients were studied. The results of our study were given in the following three aspects. Firstly, the coefficient of adaptive total variation should be verified by the properties: Moreover, Minimal surfaces function was considered to be suitable for the method. Secondly, -based image restoration algorithm was put forward, and the diffusion coefficient should be verified by the following properties: it was a decreasing functional; on high gradients the coefficient decreased to 0, low gradients to 1. Moreover, g(s)=1/ (s²+1)^1/2 was considered to be suitable for the method. Lastly, imaginary part was taken as the variable of the diffusion coefficient for nonlinear complex diffusion, and the coefficient should be verified by the following properties: when s â†'0, c ( s)â†'1; when s â†'∞, c ( s)â†'0; and the change of c (s) should not be too sharp or too slow. Comparing with the above two frameworks, the nonlinear complex diffusion with the coefficient c(s)= 1/(s+1)^1/2 was better than any of the two others.