A New Noise Removal Method Based on Fourth-Order Nonlinear Diffusion

A class of fourth-order partial differential equations(PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional, which is an increasing function of the directional curvature magnitude of the image intensity function. These PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image. Piecewise planar images look more natural than step images which (second order) nonlinear diffusion uses to approximate an observed image. So the proposed PDEs are able to avoid the blocky effects and false edges widely seen in images processed by second order nonlinear diffusion, while achieving the degree of noise removal and edge preservation comparable to second order PDEs. Other fourth-order nonlinear diffusion processes need despeckle algorithms to remove speckles after processing, while the PDEs proposed in this paper have no such problem. Since the fixed, finite spacing between pixels, “leakage” problem is common in nonlinear diffusion. Small leaks over many timesteps gradually erode the image boundaries and eventually destroy them all. In this paper a self-adjusting leakage fix for pixel is proposed, and it has been proven to be efficient in preserving details of image. As the diffusion coefficient is locally adjusted according to image features such as edges, textures and moments, FAB diffusion is introduced into the proposed PDEs. By adding the diffusion direction function in diffusion coefficient a new class of adaptive nonlinear diffusion processes named as Composite Diffusion are proposed, which can switch the diffusion process from a backward to a forward mode to smooth the pixel corrupted by impulsive noise and Gaussian noise, so the proposed Composite Diffusion processes can enhance features while locally denoising the signal or image corrupted by blended additive noises.