Convergence and performance of the peeling wavelet denoising algorithm

Céline Lacaux (1, 2) , Aurélie Muller (1, 2) , Radu Ranta (3) , Samy Tindel (1, 2)

1 BIGS - Biology, genetics and statistics
2 IECL - Institut Élie Cartan de Lorraine
3 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 useful signal are modeled by generalized Gaussian random variables and its noisy part by independent Gaussian 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 implementations are tested against classical wavelet denoising procedures on benchmark and simulated biological signals.

Mots clés: Empirical processes; Generalized Gaussian distribution; Wavelets; Denoising; Peeling algorithm

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Céline Lacaux, Aurélie Muller, Radu Ranta, Samy Tindel. Convergence and performance of the peeling wavelet denoising algorithm. Metrika, 2014, 77 (4), pp.509-537. ⟨10.1007/s00184-013-0451-y⟩. ⟨hal-00903593⟩