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Optimization and Engineering

, Volume 19, Issue 1, pp 39–70 | Cite as

Sparse \(\ell _{1}\) regularisation of matrix valued models for acoustic source characterisation

  • Laurent Hoeltgen
  • Michael Breuß
  • Gert Herold
  • Ennes Sarradj
Article
  • 103 Downloads

Abstract

We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears similarities to the basis pursuit formalism but also relies on additional model assumptions that are challenging from a mathematical point of view. Our approach reformulates the original task as a convex optimisation model. The sought solution shall be a matrix with a certain desired structure. We enforce this structure through additional constraints. By combining popular splitting algorithms and matrix differential theory in a novel framework we obtain a numerically efficient strategy. Besides a thorough theoretical consideration we also provide an experimental setup that certifies the usability of our strategy. Finally, we also address practical issues, such as the handling of inaccuracies in the measurement and corruption of the given data. We provide a post processing step that is capable of yielding an almost perfect solution in such circumstances.

Keywords

Convex optimisation Sparse recovery Split Bregman Matrix differentiation Acoustic source characterisation Microphone array 

Mathematics Subject Classification

MSC 65K10 MSC 65Z05 MSC47A99 

Notes

Acknowledgement

This work has partially been funded by the German Research Foundation (DFG) within the Grant No. SA 1502/5-1. This funding is thankfully acknowledged.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Laurent Hoeltgen
    • 1
  • Michael Breuß
    • 1
  • Gert Herold
    • 2
  • Ennes Sarradj
    • 2
  1. 1.Chair for Applied MathematicsBrandenburg University of Technology Cottbus-SenftenbergCottbusGermany
  2. 2.Institut für Strömungsmechanik und Technische AkustikTechnische Universität BerlinBerlinGermany

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