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Sparse ℓ1 regularisation of matrix valued models for acoustic source characterisation

  • 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 ofWe 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.show moreshow less

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Metadaten
Author: Laurent HoeltgenORCiD, Michael BreußGND, Gert Herold, Ennes SarradjORCiD
DOI:https://doi.org/10.1007/s11081-017-9357-2
ISSN:1389-4420
ISSN:1573-2924
Title of the source (English):Optimization and Engineering
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2018
Tag:Acoustic source characterisation; Convex optimisation; Matrix differentiation; Microphone array; Sparse recovery; Split Bregman
Volume/Year:19
Issue number:1
First Page:39
Last Page:70
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Angewandte Mathematik
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