Uniform Noise Removal Base On Maximum A Posteriori Approach

Signal denoising plays a very important role in the field of signal science.With the development of information technology,it has become particularly important to obtain highly accurate data signals.In general,signals are often contaminated by noise during the acquisition or transmission process,so that the signal quality is reduced.Therefore,in order to obtain high-precision signals,noise must be removed.The purpose of signal denoising is to extract the exact signal from the noise signal by using some denoising algorithms.A number of methods and techniques have been successfully applied to signal denoising.Selecting a nice method depends on the types of noise.Although nature noises are very complicated,three noise types are often considered in order to study the performance of denoising algorithms.The three types include a Gaussian noise,an impulse noise,and a uniform noise.The removal algorithms of Gaussian noise and impulse noise have been widely investigated.This article will mainly discuss the uniform noise removal algorithm.According to the method of statistical Maximum a posteriori approach,the problem of uniform noise removal can be expressed mathematically as a minimization problem with infinite norm constraints,and a numerical difficult arises due to the property of the non-differentiability of the infinite norm.We mainly use two algorithms to solve this difficulty with infinite norm constraints.The first algorithm uses the convex optimization theory to find the dual problem of the original problem,and then uses the forward-backward splitting method to solve the dual problem to obtain the optimal solution of the original problem.Another algorithm is to convert the original problem into two minimized sub-problems with analytical solutions by introducing a convex model function,and then solving the different sub-problems separately according to the principle of variable separation.Thus we can get an alternative iterative formula.Experimental results show that both algorithms have better results in terms of accuracy and time.