Sparse denoising of audio by greedy time-frequency shrinkage

Abstract

Matching Pursuit (MP) is a greedy algorithm that iteratively builds a sparse signal representation. This work presents an analysis of MP in the context of audio denoising. By interpreting the algorithm as a simple shrinkage approach, we identify the factors critical to its success, and propose several approaches to improve its performance and robustness. We also develop several model enhancements and introduce an audio denoising approach called Greedy Time-Frequency Shrinkage (GTFS). Numerical experiments are performed on a wide range of audio signals, and we demonstrate that GTFS denoising is able to yield results that are competitive with state-of-the-art audio denoising approaches. Notably, GTFS retains a small percentage of a signal's transform coefficients for building a denoised representation, i.e., it produces very sparse denoised results.ii Résumé L'algorithme de Matching Pursuit (MP) construit par itérations une représentation parcimonieuse du signal, au prix d'un coût de calculélevé. Ce mémoire présente une analyse de l'algorithme de MP dans le contexte du débruitage audio. En interprétant l'algorithme MP comme une méthode de contraction simple (simple shrinkage), nous chercheronsà identifier les facteurs essentielsà son succès, puis proposerons plusieurs approches afin d'en améliorer les performances et la robustesse. Plusieurs améliorations du modèle seront ainsi développées, et une approche du débruitage audio dénommée Greedy Time-Frequency Shrinkage (GTFS) sera présentée en détails. Des expérimentations numériques appliquées a un largeéventail de signaux sonores démontrent que les résultats obtenus par débruitage GTFS s'avèrent compétitifs face aux méthodes de débruitage audio qui constituent l'état de l'art. En particulier, le GTFS ne retient qu'un faible pourcentage des coefficients de la transformée du signal pour en construire une représentation débruitée, et produit ainsi des résultats débruités très compacts.iii

Interpolation and denoising of seismic signals using orthogonal matching pursuit algorithm: An aplication in VSP and refraction data

“…Sparse signal representation in overcomplete dictionaries is an analytic tool that has been satisfactorily implemented in multiple signal and image processing applications such as image compression [15], audio denoising [16], and seismic signal pre-processing [17]. Its principle basically consists in representing the signal of interest as a linear combination of a few columns from a previously specified redundant matrix called dictionary, where each column of this matrix is called an atom of the dictionary.…”

Fast Matching Pursuit with Multi-Gabor Dictionaries

“…An overview of greedy algorithms, a class of algorithms MP falls under, can be found in [37,46] and in the context of audio and music processing in [30,40,47]. Notable applications of MP algorithms include audio analysis [17], [15], coding [5,35,44], time scaling/pitch shifting [10] [43], source separation [16], denoising [2], partial and harmonic detection and tracking [24] and EEG analysis [12].…”

Audio Denoising Based on Short Time Fourier Transform

“…There are two stages are involved: first stage is used to obtain linear combination using this assumption and second stage estimates the number of remaining noise. Greedy time-frequency shrinkage based sparse audio de-noising is discussed in [3]. Matching pursuit in the background of audio de-noising is analysed.…”