On-grid compressive sampling for spherical field measurements in acoustics

Published

October 18, 2022

Author(s)

Alex Yuffa, Marc Valdez, Michael Wakin

Abstract

We derive a theoretically guaranteed compressive sensing method for acoustic field reconstructions using spherical field measurements on a predefined grid. This method can be used to reconstruct sparse band-limited spherical harmonic or Wigner $D$-function series. Contrasting typical compressive sensing methods for spherical harmonic or Wigner $D$-function series that use random measurements on the sphere or rotation group, the new method samples on an equiangular grid in those domains, which is a commonly used sampling pattern. Using the periodic extension of the Wigner $D$-functions, we transform the reconstruction of a Wigner $D$-function series (of which spherical harmonics are a special case) into a multi-dimensional Fourier domain reconstruction problem. We establish that this transformation maintains sparsity in cases of interest and provide numerical studies of the transformation's effect on sparsity. We also provide numerical studies of the reconstruction performance of the compressive sensing approach compared to classical Nyquist sampling. In the cases tested, we find accurate compressive sensing reconstructions need only a fraction of the measurements dictated by the Nyquist sampling theorem. Moreover, using one-third of the measurements or less, the compressive sensing method can provide over 20dB more denoising capabilities than oversampling with classical Fourier theory.

Citation

Journal of the Acoustical Society of America

Pub Type

Journals

Download Paper

https://doi.org/10.1121/10.0014628

Local Download

Keywords

compressive sensing, metrology, Band-limited Spherical Wavefunctions, Wigner-d functions

Citation

Yuffa, A. , Valdez, M. and Wakin, M. (2022), On-grid compressive sampling for spherical field measurements in acoustics, Journal of the Acoustical Society of America, [online], https://doi.org/10.1121/10.0014628, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=934668 (Accessed October 10, 2025)