Uniform Noise Removal Using L-infinity Norm

Signal noise removal is an important research problem in signal science. In the process of signal transmission or acquisition, it is inevitable to produce noise. Noise pollute signal, reduce the quality of the signal, and affect the visual effect of the read-er, so noise isn’t the component of the signal. Signal noise mainly include Gaussian noise, uniform noise, Poisson noise, impulse noise and so on. The original signal are often contaminated noise of the probability density functions of Gaussian distribution, uniform distribution, Poisson distribution, Laplace distribution. Different optimization models correspond to different noise. The problem of signal denoising can be trans-formed into an optimization problem including data-fitting term and regularization ter-m.Uniform noise removal is a minimization problem with L-infinity norm constraint of mathematics. A numerical difficult of minimization problem arises due to the prop-erty of the non-differentiability of the L-infinity norm. The main contribution of this paper is to propose a first order primal-dual algorithm of L-infinity norm constraint. This algorithm is classical algorithm of a saddle point of maximin problems. In order to apply a first order primal-dual algorithm for computing extremum of maximin prob-lems, the original problem can transform into maximin problems. In this paper, original problem turn into a solution of maximin problems, thus original problem can be com-puted by a first order primal-dual algorithm. The numerical results show that the root mean square error of proposed method is less than the previously algorithms and the proposed algorithm is better than the previous algorithm.