2004
DOI: 10.1109/lsp.2003.822904
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Transient Modeling by Matching Pursuits With a Wavelet Dictionary for Parametric Audio Coding

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Cited by 41 publications
(15 citation statements)
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“…Atomic signal decomposition techniques are used in many areas, such as denoising; harmonic analysis; parameter extraction; and time‐frequency decomposition . In atomic decomposition, the matrix A is considered a redundant dictionary, since it has more elements than the dimension of vector b .…”
Section: Sparse Representation Of Signalsmentioning
confidence: 99%
See 1 more Smart Citation
“…Atomic signal decomposition techniques are used in many areas, such as denoising; harmonic analysis; parameter extraction; and time‐frequency decomposition . In atomic decomposition, the matrix A is considered a redundant dictionary, since it has more elements than the dimension of vector b .…”
Section: Sparse Representation Of Signalsmentioning
confidence: 99%
“…Atomic signal decomposition techniques are used in many areas, such as denoising 16 ; harmonic analysis 17 ; parameter extraction 18 ; and time-frequency decomposition. 19 In atomic decomposition, the matrix A is considered a redundant dictionary, since it has more elements than the dimension of vector b. In this way, A has more columns than rows (M > N), and the linear system described in (1) has various solutions, and the sparse representation of the signal is the one that uses the lowest number of elements.…”
Section: Figurementioning
confidence: 99%
“…This is done by decomposing signals using an overcomplete dictionary of functions, such as Gabor dictionary [59] as used in their work. Other available dictionaries are wavelets [60], wavelet packets [61], multiscale Gabor dictionaries [62], and chirplets [63]. An overcomplete dictionary ensures that the signal converges to a solution with zero residual energy and, therefore, results in the best set of functions to approximate the original representation.…”
Section: Sparse Decompositionmentioning
confidence: 99%
“…Taking into account that only the correlations between atoms with heritage relation (i 2 = i 1 /2 j 1 −j 2 ) have to be considered when waveletDownloaded by [Florida International University] at 04:23 20 December 2014 based dictionaries built from orthonormal wavelets are used, expression (12) results in [30]:…”
Section: Transient Modeling By Matching Pursuit With a Wavelet-based mentioning
confidence: 99%