LLT Denoising Model Based On Fixed-point Proximity Algorithm

Image is a visual description of the realistic world. We use it as a common carrier to both record and describe information. With the development of information technology, image processing is getting more and more perfect, and is being successfully applied in many fields. As a crucial part of image preprocessing, image denoising has become not only a popular research subject, but also the foundation and basic module of image postprocessing technique.In this article, we first introduce the definition and history of digital image technology and the development of image processing based on PDEs. Then the explanation about the image forming model, digital image noise and its generating process is given.We reduce the form of general denoising model based on the Bayesian theory in section 1:The relation of variation methods, Euler-Lagrange equation and the solution of the energy function of denoising model is then clarified in details. We take TV model as a key point, and use local coordinate to analyze the anisortropy property of the model and briefly illustrate both the difference and the relation of two TV normal. Then we point out the advantages and disadvantages of low-order denoising model. Then high-order denoising model is introduced. Here we explain a representative model, i.e, LLT model: Both advantages and defects of high-order model are pointed out here, that is, it can effectively avoid the so-called "block-effect", which is easily appeared in low-order model, however, it also has some problems like other high-order model. At last, numerical scheme and solution of two representative models are given.In section 2, we explain the fixed-point algorithm and its related theoretical foundation. Then we illustrate the relation of approximation operators and functional minimum, according to which the fixed-point equation of LLT model is deduced: Where H is defined as follows: Then the convergence condition of fixed-point equation is given and the applicability of LLT model is explained. Then the solving strategy of fixed point equation is clarified:The results of numerical tests are shown in detail in section 4. We have done numerical experiment about LLT model based on both variation method and fixed point algorithm. Contrastive numerical tests are done in both repression of "block effect "and effect of denoising. We analyze the numerical results, which leads to the conclusion that fixed point algorithm not only inherits the excellent properties of high order equations, but also guarantees better effect of denoising, and the algorithm is more stable and fast.