Diffusion has received a lot of attention and has experienced significant developments, it can simultaneously enhance,
sharpen and denoise image. The diffusion coefficient is locally adjust according to image features such as edges, textures,
and moments, so it has many formats diffusion process according to the set of gradient. Suck as P-M diffusion and total
variation. The aim of the present paper is to study the total variation then replace the smoothed intensity function with
the P-M diffusion function and derive the fidelity term to get a novel nonlinear anisotropic P-M diffusion. And then
deduce the new diffusion application in discrete two dimension space for image denoise. The results of experiments
demonstrate the novel P-M diffusion denoise the image and retain the details more effective than traditional P-M
The diffusion process can simultaneously enhance, sharpen and denoise image. The diffusion coefficient is locally adjust according to image gradient, so it has many formats diffusion process according to the set of criteria, suck as P-M diffusion,complex diffusion and forward and backward diffusion. In the complex diffusion, the imaginary part of image serve as approximate second derivative of image. So using the imaginary to control the diffusion coefficient can combine the forward and backward complex diffusion.The forward and backward complex diffusion choice forward or backward diffusion according to the imaginary part. The forward diffusion denoise and smooth the image,and the backward diffusion magnify the noise and sharpen the edges, so the the forward and backward complex diffusion can't denoise detail part of image effectively.The shock filer sharpen the edges can take for inverse diffusion, in the paper,we use the imaginary part to control the shock filter as the backward part and the nonlinear complex diffusion as the forward part to combine a novel forward and backward complex diffusion. This novel isn't selectivity diffusion but forward and backward diffusion both diffuse simultaneously.The results of experiments demonstrate the novel denoise the image and retain the details more effective than the forward and backward complex diffusion.