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Journal of the Acoustical Society of America / Volume 123 / Issue 5 / ACOUSTIC SIGNAL PROCESSING [60]

Sparsity constrained deconvolution approaches for acoustic source mapping

J. Acoust. Soc. Am. Volume 123, Issue 5, pp. 2631-2642 (2008); (12 pages)

Tarik Yardibi1, Jian Li1, Petre Stoica2, and Louis N. Cattafesta, III3

1Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida, 32611
2Department of Information Technology, Uppsala University, P.O. Box 337, SE-751 05 Uppsala, Sweden
3Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida, 32611

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Using microphone arrays for estimating source locations and strengths has become common practice in aeroacoustic applications. The classical delay-and-sum approach suffers from low resolution and high sidelobes and the resulting beamforming maps are difficult to interpret. The deconvolution approach for the mapping of acoustic sources (DAMAS) deconvolution algorithm recovers the actual source levels from the contaminated delay-and-sum results by defining an inverse problem that can be represented as a linear system of equations. In this paper, the deconvolution problem is carried onto the sparse signal representation area and a sparsity constrained deconvolution approach (SC-DAMAS) is presented for solving the DAMAS inverse problem. A sparsity preserving covariance matrix fitting approach (CMF) is also presented to overcome the drawbacks of the DAMAS inverse problem. The proposed algorithms are convex optimization problems. Our simulations show that CMF and SC-DAMAS outperform DAMAS and as the noise in the measurements increases, CMF works better than both DAMAS and SC-DAMAS. It is observed that the proposed algorithms converge faster than DAMAS. A modification to SC-DAMAS is also provided which makes it significantly faster than DAMAS and CMF. For the correlated source case, the CMF-C algorithm is proposed and compared with DAMAS-C. Improvements in performance are obtained similar to the uncorrelated case.

© 2008 Acoustical Society of America

ACKNOWLEDGMENTS

This work was supported in part by NASA under Grant No. NNX07AO15A and the Swedish Science Council (VR).

Article Outline

  1. INTRODUCTION
  2. PROBLEM FORMULATION
  3. REVIEW OF DAMAS
  4. SPARSITY CONSTRAINED DAMAS (SC-DAMAS)
    1. Sparsity constrained formulation
    2. Estimating the user parameter
    3. A more efficient implementation of SC-DAMAS
  5. COVARIANCE MATRIX FITTING
  6. CORRELATED SOURCES
    1. DAMAS-C
    2. CMF-C
  7. NUMERICAL EXAMPLES
  8. CONCLUSIONS

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KEYWORDS and PACS

Keywords

acoustic signal processing, aeroacoustics, array signal processing, covariance matrices, deconvolution, inverse problems, microphone arrays, signal representation

PACS

  • 43.60.Fg

    Acoustic array systems and processing, beam-forming

  • 43.60.Jn

    Source localization and parameter estimation

  • 43.60.Pt

    Signal processing techniques for acoustic inverse problems

  • 43.60.Mn

    Adaptive processing

ARTICLE DATA

History
Received 02 Nov 2007
Accepted 14 Feb 2008
Revised 11 Feb 2008
Digital Object Identifier
http://dx.doi.org/10.1121/1.2896754

PUBLICATION DATA

ISSN

0001-4966 (print)  

Publisher

$abstract.society.value is a Member of CrossRef Acoustical Society of America

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