Blind source separation by sparse decomposition in a signal dictionary

Zibulevsky, Michael; Pearlmutter, Barak A.; Bofill, Pau; Kisilev, Pavel

doi:10.1017/cbo9780511624148.008

Cited by 304 publications

(479 citation statements)

References 104 publications

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“…• Empirical work, showing that combined representations such as wavelets with curvelets or wavelets with sinusoids often gave very compelling separations of real signals and images, see, for instance, [1,10,25,26,35,42,40,41,43,44,30,47].…”

Section: Minimum ℓ 1 Decomposition and Perfect Separationmentioning

confidence: 99%

Microlocal Analysis of the Geometric Separation Problem

Donoho

Kutyniok

2012

Comm Pure Appl Math

190

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Image data are often composed of two or more geometrically distinct constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike structures (galaxy superclusters) and curvelike structures (filaments). It would be ideal to process a single image and extract two geometrically 'pure' images, each one containing features from only one of the two geometric constituents. This seems to be a seriously underdetermined problem, but recent empirical work achieved highly persuasive separations.We present a theoretical analysis showing that accurate geometric separation of point and curve singularities can be achieved by minimizing the ℓ 1 norm of the representing coefficients in two geometrically complementary frames: wavelets and curvelets. Driving our analysis is a specific property of the ideal (but unachievable) representation where each content type is expanded in the frame best adapted to it. This ideal representation has the property that important coefficients are clustered geometrically in phase space, and that at fine scales, there is very little coherence between a cluster of elements in one frame expansion and individual elements in the complementary frame. We formally introduce notions of cluster coherence and clustered sparsity and use this machinery to show that the underdetermined systems of linear equations can be stably solved by ℓ 1 minimization; microlocal phase space helps organize the calculations that cluster coherence requires.

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Section: Minimum ℓ 1 Decomposition and Perfect Separationmentioning

confidence: 99%

Microlocal Analysis of the Geometric Separation Problem

Donoho

Kutyniok

2012

Comm Pure Appl Math

190

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“…It has been shown that when sources are sparse, they can be easily recovered from their linear mixtures using simple geometrical methods [2], [5]. This is based on the observation that whenever sources are sparse, there is a high probability that each data point in each mixture will result from the contribution of only one source.…”

Section: Sparse Ica (Spica)mentioning

confidence: 99%

Blind Separation of Spatio-temporal Data Sources

Unger

Zeevi

2004

Independent Component Analysis and Blind Signal Separation

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Abstract. ICA and similar techniques have been previously applied to either one-dimensional signals or still images. We consider the problem of blind separation of dynamic sources, i.e. functions of both time and two spatial variables. We extend the Sparse ICA (SPICA) approach and apply it to a sliding data cube, defined by the two dimensions of the visual scene and the extent in time over which the mixing problem can be considered to be stationary and linear. This framework and formalism are applied to two special problems encountered in two different fields: The first deals with separation of dynamic reflections from a desired moving visual scene, without having any a priori knowledge on the structure of the images and/or their statistics. The second problem concerns blind separation of 'neural cliques' from the background firing activity of a neural network. The approach is generic in that it is applicable to any linearly mixed dynamic sources.

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“…In the audio domain, sparse prior distributions are usually a Laplacian [1], a generalized Gaussian [2], a Student-t [3], or a mixture of two Gaussians [4].…”

Section: Introductionmentioning

confidence: 99%

“…In each time-frequency point, the maximum number of nonzero sources is usually assumed to be limited to the number M of channels [1,2]. 2.…”

Section: Introductionmentioning

confidence: 99%

Blind Spectral-GMM Estimation for Underdetermined Instantaneous Audio Source Separation

Arberet

Ozerov

Gribonval

et al. 2009

Independent Component Analysis and Signal Separation

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Abstract. The underdetermined blind audio source separation problem is often addressed in the time-frequency domain by assuming that each time-frequency point is an independently distributed random variable. Other approaches which are not blind assume a more structured model, like the Spectral Gaussian Mixture Models (Spectral-GMMs), thus exploiting statistical diversity of audio sources in the separation process. However, in this last approach, Spectral-GMMs are supposed to be learned from some training signals. In this paper, we propose a new approach for learning Spectral-GMMs of the sources without the need of using training signals. The proposed blind method significantly outperforms state-of-the-art approaches on stereophonic instantaneous music mixtures.

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Blind source separation by sparse decomposition in a signal dictionary

Cited by 304 publications

References 104 publications

Microlocal Analysis of the Geometric Separation Problem

Microlocal Analysis of the Geometric Separation Problem

Blind Separation of Spatio-temporal Data Sources

Blind Spectral-GMM Estimation for Underdetermined Instantaneous Audio Source Separation

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