A sparse signal reconstruction perspective for source localization with sensor arrays

We present a source localization method based on a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold. We enforce sparsity by imposing penalties based on the /spl lscr//sub 1/-norm. A number of recent theoretical results on sparsifying...

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Bibliographic Details
Published in:	IEEE transactions on signal processing 2005-08, Vol.53 (8), p.3010-3022
Main Authors:	Malioutov, D., Cetin, M., Willsky, A.S.
Format:	Article
Language:	eng
Subjects:	Acoustic sensors Applied sciences Array signal processing Arrays Constraining Detection, estimation, filtering, equalization, prediction Direction-of-arrival estimation Estimates Exact sciences and technology Information, signal and communications theory Localization Localization method Maximum likelihood estimation Multiple signal classification overcomplete representation Position (location) Representations sensor array processing Sensor arrays Signal and communications theory Signal reconstruction Signal representations Signal resolution Signal, noise Singular value decomposition source localization sparse representation Spatial resolution superresolution Telecommunications and information theory
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Summary:	We present a source localization method based on a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold. We enforce sparsity by imposing penalties based on the /spl lscr//sub 1/-norm. A number of recent theoretical results on sparsifying properties of /spl lscr//sub 1/ penalties justify this choice. Explicitly enforcing the sparsity of the representation is motivated by a desire to obtain a sharp estimate of the spatial spectrum that exhibits super-resolution. We propose to use the singular value decomposition (SVD) of the data matrix to summarize multiple time or frequency samples. Our formulation leads to an optimization problem, which we solve efficiently in a second-order cone (SOC) programming framework by an interior point implementation. We propose a grid refinement method to mitigate the effects of limiting estimates to a grid of spatial locations and introduce an automatic selection criterion for the regularization parameter involved in our approach. We demonstrate the effectiveness of the method on simulated data by plots of spatial spectra and by comparing the estimator variance to the Crame/spl acute/r-Rao bound (CRB). We observe that our approach has a number of advantages over other source localization techniques, including increased resolution, improved robustness to noise, limitations in data quantity, and correlation of the sources, as well as not requiring an accurate initialization.
ISSN:	1053-587X 1941-0476