Removing uniform noises by using an L^∞ fitting with wavelets

In this paper, we consider a signal denoising algorithm for removing uniform noises. We use an L^∞ fitting to denoise signals due to its connection with the maximum likelihood estimator of uniform noises. We introduce a Moreau-Yosida approximation to overcome the non-differentiability of an L^∞ norm. To improve the accuracy of the L^∞ fitting, we integrate a wavelet method with this fitting. An adaptive method is designed to speed up the proposed algorithm. Numerical results on a seismic signal show that the algorithm is accurate and stable.