Convergence and performances of the peeling wavelet denoising algorithm

Céline Lacaux (1) , Aurélie Muller (1) , Radu Ranta (2) , Samy Tindel (1)

1 BIGS - Biology, genetics and statistics
2 CRAN - Centre de Recherche en Automatique de Nancy

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.

Mots clés: denoising; generalized Gaussian distribution; Wavelets; peeling algorithm; empirical processes

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Céline Lacaux, Aurélie Muller, Radu Ranta, Samy Tindel. Convergence and performances of the peeling wavelet denoising algorithm. Metrika, 2014, 77 (4), pp.509-537. ⟨10.1007/s00184-013-0451-y⟩. ⟨hal-00433888⟩