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55
A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm
, 2009
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Efficient Implementation of the KSVD Algorithm using Batch Orthogonal Matching Pursuit
"... The KSVD algorithm is a highly effective method of training overcomplete dictionaries for sparse signal representation. In this report we discuss an efficient implementation of this algorithm, which both accelerates it and reduces its memory consumption. The two basic components of our implementati ..."
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Cited by 53 (1 self)
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The KSVD algorithm is a highly effective method of training overcomplete dictionaries for sparse signal representation. In this report we discuss an efficient implementation of this algorithm, which both accelerates it and reduces its memory consumption. The two basic components of our implementation are the replacement of the exact SVD computation with a much quicker approximation, and the use of the BatchOMP method for performing the sparsecoding operations. BatchOMP, which we also present in this report, is an implementation of the Orthogonal Matching Pursuit (OMP) algorithm which is specifically optimized for sparsecoding large sets of signals over the same dictionary. The BatchOMP implementation is useful for a variety of sparsitybased techniques which involve coding large numbers of signals. In the report, we discuss the BatchOMP and KSVD implementations and analyze their complexities. The report is accompanied by Matlab Ⓡ toolboxes which implement these techniques, and can be downloaded at
Instrumentspecific harmonic atoms for midlevel music representation
 IEEE Trans. on Audio, Speech and Lang. Proc
, 2008
"... Abstract—Several studies have pointed out the need for accurate midlevel representations of music signals for information retrieval and signal processing purposes. In this paper, we propose a new midlevel representation based on the decomposition of a signal into a small number of sound atoms or m ..."
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Cited by 41 (6 self)
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Abstract—Several studies have pointed out the need for accurate midlevel representations of music signals for information retrieval and signal processing purposes. In this paper, we propose a new midlevel representation based on the decomposition of a signal into a small number of sound atoms or molecules bearing explicit musical instrument labels. Each atom is a sum of windowed harmonic sinusoidal partials whose relative amplitudes are specific to one instrument, and each molecule consists of several atoms from the same instrument spanning successive time windows. We design efficient algorithms to extract the most prominent atoms or molecules and investigate several applications of this representation, including polyphonic instrument recognition and music visualization. Index Terms—Midlevel representation, music information retrieval, music visualization, sparse decomposition. I.
1 Sparse Representations in Audio and Music: from Coding to Source Separation
"... Abstract—Sparse representations have proved a powerful tool in the analysis and processing of audio signals and already lie at the heart of popular coding standards such as MP3 and Dolby AAC. In this paper we give an overview of a number of current and emerging applications of sparse representations ..."
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Cited by 37 (9 self)
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Abstract—Sparse representations have proved a powerful tool in the analysis and processing of audio signals and already lie at the heart of popular coding standards such as MP3 and Dolby AAC. In this paper we give an overview of a number of current and emerging applications of sparse representations in areas from audio coding, audio enhancement and music transcription to blind source separation solutions that can solve the “cocktail party problem”. In each case we will show how the prior assumption that the audio signals are approximately sparse in some timefrequency representation allows us to address the associated signal processing task. I.
Shiftinvariant dictionary learning for sparse representations: extending KSVD
 in Proc. EUSIPCO
, 2008
"... Shiftinvariant dictionaries are generated by taking all the possible shifts of a few short patterns. They are helpful to represent long signals where the same pattern can appear several times at different positions. We present an algorithm that learns shift invariant dictionaries from long training ..."
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Cited by 27 (2 self)
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Shiftinvariant dictionaries are generated by taking all the possible shifts of a few short patterns. They are helpful to represent long signals where the same pattern can appear several times at different positions. We present an algorithm that learns shift invariant dictionaries from long training signals. This algorithm is an extension of KSVD. It alternates a sparse decomposition step and a dictionary update step. The update is more difficult in the shiftinvariant case because of occurrences of the same pattern that overlap. We propose and evaluate an unbiased extension of the method used in KSVD, i.e. a method able to exactly retrieve the original dictionary in a noiseless case. 1.
Union of MDCT bases for audio coding
 IEEE Trans. on Audio, Speech and Lang. Proc
, 2008
"... Abstract—This paper investigates the use of sparse overcomplete decompositions for audio coding. Audio signals are decomposed over a redundant union of modified discrete cosine transform (MDCT) bases having eight different scales. This approach produces a sparser decomposition than the traditional M ..."
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Cited by 19 (7 self)
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Abstract—This paper investigates the use of sparse overcomplete decompositions for audio coding. Audio signals are decomposed over a redundant union of modified discrete cosine transform (MDCT) bases having eight different scales. This approach produces a sparser decomposition than the traditional MDCTbased orthogonal transform and allows better coding efficiency at low bitrates. Contrary to stateoftheart low bitrate coders, which are based on pure parametric or hybrid representations, our approach is able to provide transparency. Moreover, we use a bitplane encoding approach, which provides a finegrain scalable coder that can seamlessly operate from very low bitrates up to transparency. Objective evaluation, as well as listening tests, show that the performance of our coder is significantly better than a stateoftheart transform coder at very low bitrates and has similar performance at high bitrates. We provide a link to test soundfiles and source code to allow better evaluation and reproducibility of the results. Index Terms—Audio coding, matching pursuit, scalable coding, signal representations, sparse representations.
Convergence of a Sparse Representations Algorithm Applicable to Real or Complex Data
 IEEE Journ. of STSP
, 2007
"... Abstract—Sparse representations has become an important topic in recent years. It consists in representing, say, a signal (vector) as a linear combination of as few as possible components (vectors) from a redundant basis (of the vector space). This is usually performed, either iteratively (adding a ..."
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Cited by 13 (2 self)
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Abstract—Sparse representations has become an important topic in recent years. It consists in representing, say, a signal (vector) as a linear combination of as few as possible components (vectors) from a redundant basis (of the vector space). This is usually performed, either iteratively (adding a component at a time), or globally (selecting simultaneously all the needed components). We consider a specific algorithm, that we obtain as a fixed point algorithm, but that can also be seen as an iteratively reweighted leastsquares algorithm. We analyze it thoroughly and show that it converges to the global optimum. We detail the proof in the real case and indicate how to extend it to the complex case. We illustrate the result with some easily reproducible toy simulations, that further illustrate the potential tracking properties of the proposed algorithm. Index Terms—Convergence of numerical methods, fixedpoint algorithms, iterative methods, minimization methods, spectral analysis. I.
Analysis and Synthesis of PseudoPeriodic Job Arrivals in Grids: A Matching Pursuit Approach
 In Proceedings of the Seventh IEEE International Symposium on Cluster Computing and the Grid, Rio De Janeiro
, 2007
"... Pseudoperiodicity is one of the basic job arrival patterns on dataintensive clusters and Grids. In this paper, a signal decomposition methodology called matching pursuit is applied for analysis and synthesis of pseudoperiodic job arrival processes. The matching pursuit decomposition is well lo ..."
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Cited by 11 (6 self)
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Pseudoperiodicity is one of the basic job arrival patterns on dataintensive clusters and Grids. In this paper, a signal decomposition methodology called matching pursuit is applied for analysis and synthesis of pseudoperiodic job arrival processes. The matching pursuit decomposition is well localized both in time and frequency, and it is naturally suited for analyzing nonstationary as well as stationary signals. The stationarity of the processes can be quantitatively measured by permutation entropy, with which the relationship between stationarity and modeling complexity is excellently explained. Quantitative methods based on the power spectrum are also provided to measure the degree of periodicity present in the data. Matching pursuit is further shown to be able to extract patterns from signals, which is an attractive feature from a modeling perspective. Real world workload data from production clusters and Grids are used to empirically evaluate the proposed measures and methodologies. 1
An Iterative Bayesian Algorithm for Sparse Component Analysis in Presence of Noise
, 2009
"... We present a Bayesian approach for Sparse Component Analysis (SCA) in the noisy case. The algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations with additive Gaussian noise. In general, an underdetermined system of linear equatio ..."
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Cited by 9 (1 self)
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We present a Bayesian approach for Sparse Component Analysis (SCA) in the noisy case. The algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations with additive Gaussian noise. In general, an underdetermined system of linear equations has infinitely many solutions. However, it has been shown that sufficiently sparse solutions can be uniquely identified. Our main objective is to find this unique solution. Our method is based on a novel estimation of source parameters and maximum a posteriori (MAP) estimation of sources. To tackle the great complexity of the MAP algorithm (when the number of sources and mixtures become large), we propose an Iterative Bayesian Algorithm (IBA). This IBA algorithm is based on the MAP estimation of sources, too, but optimized with a steepestascent method. The convergence analysis of the IBA algorithm and its convergence to true global maximum are also proved. Simulation results show that the performance achieved by the IBA algorithm is among the best, while its complexity is rather high in comparison to other algorithms. Simulation results also show the low sensitivity of the IBA algorithm to its simulation parameters.