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Sparse Recovery of Sound Fields Using Measurements from Moving Microphones

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Compressed Sensing in Information Processing

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

For collecting spatially dense sound-field data over an extended volume, the use of moving microphones is an efficient alternative compared to stationary methods. Samples taken at continuously varying positions encode parameters that describe the particular sound field in the measurement volume. Parameter decoding imposes a deconvolution problem in the time dimension and an interpolation problem in the spatial dimension, which can be both integrated into a system of linear equations. For larger bandwidths, the original multidimensional sampling problem tends to be ill-posed or even underdetermined unless an excessive number of samples are provided. In such cases, sparse recovery is the key. This chapter recapitulates ideas and strategies of a recently developed framework that exploits sparsity and inherent structure of the sound-field spectrum, in order to obtain qualified parameter estimates according to the compressed-sensing paradigm. The framework is based on a sound-field representation by notional grid points in space, and dynamic samples are interpreted as the result of bandlimited interpolation on that grid using sampled sinc-function approximations. This procedure leads to a highly structured sensing matrix that allows us to accomplish tasks such as recovery, coherence analysis, and trajectory optimization at low computational effort.

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Authors and Affiliations

  1. Institute for Signal Processing, University of Lübeck, Lübeck, Germany

    Fabrice Katzberg & Alfred Mertins

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  1. Fabrice Katzberg
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  2. Alfred Mertins
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Correspondence to Alfred Mertins .

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Editors and Affiliations

  1. Mathematisches Institut, Ludwig Maximilian University of Munich, München, Bayern, Germany

    Gitta Kutyniok

  2. Lehrstuhl für Mathematik, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Holger Rauhut

  3. Lehrstuhl für Mathematik, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Robert J. Kunsch

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Katzberg, F., Mertins, A. (2022). Sparse Recovery of Sound Fields Using Measurements from Moving Microphones. In: Kutyniok, G., Rauhut, H., Kunsch, R.J. (eds) Compressed Sensing in Information Processing. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-09745-4_15

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