Enhancing sparsity in linear prediction of speech by iteratively reweighted 1-norm minimization

Giacobello, Daniele; Christensen, Mads Græsbøll; Murthi, Manohar N.; Jensen, Søren Holdt; Moonen, Marc

doi:10.1109/icassp.2010.5495198

Cited by 17 publications

(28 citation statements)

References 14 publications

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“…The L 1 norm minimization may be iteratively re-weighted to obtain better results. Despite the increase of complexity, this approach is very promising [28].…”

Section: Methods Based On the Minimization Of The L 1 Normmentioning

confidence: 99%

Greedy sparse decompositions: a comparative study

Dymarski

Moreau

Richard

2011

EURASIP J. Adv. Signal Process.

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The purpose of this article is to present a comparative study of sparse greedy algorithms that were separately introduced in speech and audio research communities. It is particularly shown that the Matching Pursuit (MP) family of algorithms (MP, OMP, and OOMP) are equivalent to multi-stage gain-shape vector quantization algorithms previously designed for speech signals coding. These algorithms are comparatively evaluated and their merits in terms of trade-off between complexity and performances are discussed. This article is completed by the introduction of the novel methods that take their inspiration from this unified view and recent study in audio sparse decomposition.

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“…The L 1 norm minimization may be iteratively re-weighted to obtain better results. Despite the increase of complexity, this approach is very promising [28].…”

Section: Methods Based On the Minimization Of The L 1 Normmentioning

confidence: 99%

Greedy sparse decompositions: a comparative study

Dymarski

Moreau

Richard

2011

EURASIP J. Adv. Signal Process.

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“…As this problem is an N-P hard http://asmp.eurasipjournals.com/content/2013/1/3 optimization problem [8], its relaxed but more tractable versions (p = 1, 2) are the most widely used.…”

Section: Approaching the L 0 -Normmentioning

confidence: 99%

“…The l 1 -norm minimization of residuals is already proven to be beneficial for speech processing [6][7][8]. In [6], the stability issue of l 1 -norm linear programming is addressed and a method is introduced for both having an intrinsically stable solution as well as keeping the computational cost down.…”

Section: Introductionmentioning

confidence: 99%

“…It is argued in [3] that the reason behind the failure of the classical method in providing such sparse representation is that it relies on the minimization of l 2 -norm of prediction error. It is known that the l 2 -norm criterion is highly sensitive to the outliers [4], i.e., the points having considerably larger norms of error.…”

Section: Introductionmentioning

confidence: 99%

“…Later, they have proposed a re-weighted l 1 -norm minimization approach in [8], to enhance the sparsity of the residuals and to overcome the mismatch between l 0 -norm minimization and l 1 -norm minimization while keeping the problem solvable with convex programming tools. Initially the l 1 -norm minimization problem is solved using the interior points method and then the resulted residuals are used iteratively, to re-weight the l 1 -norm objective function such that less weight is given to the points having larger residual norms.…”

Section: Introductionmentioning

confidence: 99%

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An efficient solution to sparse linear prediction analysis of speech

Khanagha

Daoudi

2013

J AUDIO SPEECH MUSIC PROC.

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We propose an efficient solution to the problem of sparse linear prediction analysis of the speech signal. Our method is based on minimization of a weighted l 2 -norm of the prediction error. The weighting function is constructed such that less emphasis is given to the error around the points where we expect the largest prediction errors to occur (the glottal closure instants) and hence the resulting cost function approaches the ideal l 0 -norm cost function for sparse residual recovery. We show that the efficient minimization of this objective function (by solving normal equations of linear least squares problem) provides enhanced sparsity level of residuals compared to the l 1 -norm minimization approach which uses the computationally demanding convex optimization methods. Indeed, the computational complexity of the proposed method is roughly the same as the classic minimum variance linear prediction analysis approach. Moreover, to show a potential application of such sparse representation, we use the resulting linear prediction coefficients inside a multi-pulse synthesizer and show that the corresponding multi-pulse estimate of the excitation source results in slightly better synthesis quality when compared to the classical technique which uses the traditional non-sparse minimum variance synthesizer.

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Efficient GCI Detection for Efficient Sparse Linear Prediction

Khanagha

Daoudi

2013

Advances in Nonlinear Speech Processing

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Abstract. We propose a unified non-linear approach that offers an efficient closed-form solution for the problem of sparse linear prediction analysis. The approach is based on our previous work for minimization of the weighted l2-norm of the prediction error. The weighting of the l2-norm is done in a way that less emphasis is given to the prediction error around the Glottal Closure Instants (GCI) as they are expected to attain the largest values of error and hence, the resulting cost function approaches the ideal l0-norm cost function for sparse residual recovery. As such, the method requires knowledge of the GCIs. In this paper we use our recently developed GCI detection algorithm which is particularly suitable for this problem as it does not rely on residuals themselves for detection of GCIs. We show that our GCI detection algorithm provides slightly better sparsity properties in comparison to a recent powerful GCI detection algorithm. Moreover, as the computational cost of our GCI detection algorithm is quite low, the computational cost of the overall solution is considerably lower.

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Enhancing sparsity in linear prediction of speech by iteratively reweighted 1-norm minimization

Cited by 17 publications

References 14 publications

Greedy sparse decompositions: a comparative study

Greedy sparse decompositions: a comparative study

An efficient solution to sparse linear prediction analysis of speech

Efficient GCI Detection for Efficient Sparse Linear Prediction

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