Dark Energy in Sparse Atomic Estimations

Sturm, Bob L.; Shynk, J.J.; Daudet, Laurent; Roads, Curtis

doi:10.1109/tasl.2007.914975

Cited by 16 publications

(27 citation statements)

References 17 publications

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“…We also note that short atoms are more likely to be matched to noisy audio. Mismatch between dictionary atoms and a sound can lead to audible artifacts such as pre-echo [37]. In the case of noisy sounds, we found that a greedy iterative procedure often produces a signal distortion commonly known as musical noise.…”

Section: Greedy Parameter Estimationmentioning

confidence: 95%

Sparse denoising of audio by greedy time-frequency shrinkage

Bhattacharya

Depalle

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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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

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Section: Greedy Parameter Estimationmentioning

confidence: 95%

Sparse denoising of audio by greedy time-frequency shrinkage

Bhattacharya

Depalle

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…The arrows labeled "2" point to atoms at frequencies that do not exist in the original signal; and the arrows labeled "3" point to atoms at times where the original signal has no energy. These "spurious" terms reveal less about the original signal, and more about the way it is represented [Jaggi et al, 1998, Gribonval et al, 1996, Goodwin and Vetterli, 1999, Sturm, 2009, Sturm et al, 2008b. They can be seen as selfcorrection by the pursuit for atoms that are mismatched to the signal, or atoms that have been poorly selected.…”

Section: Artifacts Of Greedy Iterative Descent Methodsmentioning

confidence: 99%

“…Because of the non-orthogonal nature of the dictionaries typically used in DBMs, atoms may interact with each other in the model (6) of a signal [Sturm et al, 2008b, Sturm et al, 2008a, Sturm, 2009. In the most extreme case, an atom of a representation will completely disappear in the resynthesis through destructive interference with other atoms.…”

Section: Dark Energy and Interferencementioning

confidence: 99%

“…7. Because of this effect we call all interaction exhibited by a non-orthogonal representation dark energy [Sturm et al, 2008b, Sturm et al, 2007. Such terms are created by the decomposition algorithm to correct for "poor" atom choices made in earlier iterations, and mismatches between the signal and its model.…”

Section: Dark Energy and Interferencementioning

confidence: 99%

“…We have instead sought ways to productively use this behavior to learn about the signal and its relationship to the dictionary, and to measure the efficiency and meaningfulness of a decomposition, and the effective-ness of a pursuit [Sturm et al, 2008b, Sturm et al, 2007, Sturm et al, 2008a, Sturm, 2009. Instead of selecting atoms based on (8) for MP and OMP, or (10) for OOMP, atoms are selected with considerations of interference, for example in MP and OMP [Sturm, 2009, Sturm andShynk, 2008]:…”

Section: Dark Energy and Interferencementioning

confidence: 99%

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Analysis, Visualization, and Transformation of Audio Signals Using Dictionary-based Methods^†

Sturm

Roads

McLeran

et al. 2009

Journal of New Music Research

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In this article we provide an overview of dictionary-based methods (DBMs) -also called sparse approximation -and review recent work in the application of such methods to working with signals, in particular audio and music signals. As Fourier analysis is to additive synthesis, DBMs can be seen as the analytical counterpart to granular synthesis since a signal is rebuilt by a linear combination of heterogeneous atoms selected from a user-defined dictionary. We demonstrate how DBMs provide novel means for analyzing, visualizing, and transforming audio signals by creating multiresolution and parametric descriptions of their contents.

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