Convergence and performances of the peeling wavelet denoising algorithm

TL;DR

This paper analyzes the convergence and performance of the peeling wavelet denoising algorithm, deriving thresholds and optimal steps, and compares it with classical methods on benchmark signals.

Contribution

It provides a theoretical analysis of the peeling algorithm's convergence, thresholds, and optimal steps, with empirical validation against classical wavelet denoising.

Findings

Derived a critical thresholding constant based on the generalized Gaussian model.

Quantified the optimal number of steps for the algorithm.

Demonstrated competitive performance on benchmark and biological signals.

Abstract

This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding constant for the algorithm, which depends on the shape parameter of the generalized Gaussian distribution. We also quantify the optimal number of steps which have to be performed, and analyze the convergence of the algorithm. Several versions of the obtained algorithm were implemented and tested against classical wavelet denoising procedures on benchmark and simulated biological signals.