Simplified algorithm of signal recovery by wavelet transform maxima and its application

In this paper, an iterative projection operator for signal recovery by WT maxima is proposed. It is analytically constructed by using the principle of contraction mapping and based on the method of projections onto convex sets (POCS) in Hilbert space. This note presents a Lagrange interpolation method for de-noising noisy data in the wavelet domain, based on the frequency character of the wavelet transform to reconstruct low scale wavelet transform maxima. The effectiveness of the method is verified with practical speech signal de-noising and enhancement.