Research On Image Denoising Based On Partial Differential Equations

In the engineering practice, as the imperfection of equipments and the physical constraints,the images is inevitably subject to the interference of various noise in the process ofacquisition, transmission and storage, resulting in image degradation. This is not only affectthe visual effect of the image seriously, but also bring some difficulties to the subsequentimage processing and analysis, so denoising is one of the main contents of the imagepreprocessing，and the quality of denoising directly affect the subsequent image processing.In the denoising processes, the preservation of the image edge and texture and the noiseremoval is a contradiction. The traditional denoising algorithms would undermine the imageedge, texture and other details when removing noise. While，the denoising algorithm based onpartial differential equations, in particular, the anisotropic diffusion model, which makeselective smoothing, is able to resolve this contradiction perfectly.The partial differential equations image denoising model was researched by thecombination of theoretical analysis and simulation experiments in this paper. The specificwork is organized as follows:1. This paper analyzes the diffusion mechanism of the P-M model, considered from theintensity of diffusion and the protection of details, we make the following two improvement:(1).Change the diffusion coefficient of the partial differential equations. Making thecombination of the gradient and the variance as an intrinsic mechanism of the identification ofimage local details, thus it can identify the image details better and overcome themisjudgment phenomenon which makes the gradient as the unique identification standards.(2).Increasing the second-order time partial derivatives, and introducing the parabolichyperbolic partial differential equations which have a stronger edge detection capabilities.Finally, we proposed“an improved hyperbolic parabolic PDE model”. Experimental results show that the improved model has better denoising effect; it can not only filter out the noiseeffectively, but can also protect the edge and texture details of the image better.2. On the basis of the TV model and fourth-order PDE model, combining with thefractional partial differential theory, we proposed“an adaptive anisotropic diffusion denoisingmodel based on fractional derivative”, which is another emphasis in this paper. Theexperimental results show that the new model can effectively maintain the image edge andtexture details while removes noise, and overcomes the "staircase" effect the of TV modeland the uneven phenomenon in the flat areas of the fourth-order PDE.3. We made simulation of the above models on MATLAB7.0, and we assessed the imagequality by subjective and objective evaluation method.