A New Wavelet-TV Denoising With Non-convex Sparse Regularization

It is well known that signal denoising is important in information processing. The wavelet theory of wavelet threshold denoising and partial differential equation has been widespread in recent years due to its excellent performance in signal and image processing. This paper aims to establish a new threshold function based on Stein’s Unbiased MSE Estimate (SURE) wavelet threshold theory. In total variation denoising method, this paper shows the basic theory of total variation (TV) denoising, and adjusts the regularization parameter in total variation using non-convex regularization.The drawback of wavelet thresholding is that often introduces artifacts such as spurious noise spikes and pseudo-Gibbs oscillations around discontinuities. However, total variation (TV) denoising does not introduce such artifacts, but it often produces undesirable staircase artifacts. So, this paper aims to design a new refined wavelet denoising algorithm combining wavelet-domain sparsity and total variation with non-convex sparse regularization. To promote sparsity more strongly, the proposed approach use two non-convex penalty functions. To ensure that the objective algorithm is convex optimization, conditions are given for the non-convex regularization. The objective function restrains pseudo-Gibbs oscillations effectively. The example is presented to illustrate the effectiveness and flexibility of the method.