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Robust Sparse Component Analysis Based on a Generalized Hough Transform

EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 052105 (2006) Cite this article

Abstract

An algorithm called Hough SCA is presented for recovering the matrix in, where is a multivariate observed signal, possibly is of lower dimension than the unknown sources. They are assumed to be sparse in the sense that at every time instant, has fewer nonzero elements than the dimension of. The presented algorithm performs a global search for hyperplane clusters within the mixture space by gathering possible hyperplane parameters within a Hough accumulator tensor. This renders the algorithm immune to the many local minima typically exhibited by the corresponding cost function. In contrast to previous approaches, Hough SCA is linear in the sample number and independent of the source dimension as well as robust against noise and outliers. Experiments demonstrate the flexibility of the proposed algorithm.

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Authors and Affiliations

  1. Institute of Biophysics, University of Regensburg, Regensburg, 93040, Germany

    Fabian J. Theis

  2. ECECS Department and Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221, USA

    Pando Georgiev

  3. BSI RIKEN, Laboratory for Advanced Brain Signal Processing, 2-1, Hirosawa, Wako, Saitama, 351-0198, Japan

    Andrzej Cichocki

  4. Faculty of Electrical Engineering, Warsaw University of Technology, Pl. Politechniki 1, Warsaw, 00-661, Poland

    Andrzej Cichocki

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  1. Fabian J. Theis
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  2. Pando Georgiev
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  3. Andrzej Cichocki
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Correspondence to Fabian J. Theis.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Theis, F.J., Georgiev, P. & Cichocki, A. Robust Sparse Component Analysis Based on a Generalized Hough Transform. EURASIP J. Adv. Signal Process. 2007, 052105 (2006). https://doi.org/10.1155/2007/52105

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