Open Access

Robust Sparse Component Analysis Based on a Generalized Hough Transform

EURASIP Journal on Advances in Signal Processing20062007:052105

https://doi.org/10.1155/2007/52105

Received: 21 October 2005

Accepted: 11 June 2006

Published: 2 October 2006

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’ Affiliations

(1)
Institute of Biophysics, University of Regensburg
(2)
ECECS Department and Department of Mathematical Sciences, University of Cincinnati
(3)
BSI RIKEN, Laboratory for Advanced Brain Signal Processing
(4)
Faculty of Electrical Engineering, Warsaw University of Technology

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Copyright

© Fabian J. Theis et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.