Multipolar Acoustic Source Reconstruction from Sparse Far-Field Data Using ALOHA

Guo Y. Khan S. Wahab A. Wang X.
2023 Institute of Electrical and Electronics Engineers Inc.

IEEE Signal Processing Letters
2023 #30 1627 - 1631 pp.

The reconstruction of multipolar acoustic or electromagnetic sources from their far-field signature plays a crucial role in numerous applications. Most of the existing techniques require dense multi-frequency data at the Nyquist sampling rate. The availability of a sub-sampled grid contributes to the null space of the inverse source-to-data operator, which causes significant imaging artifacts. For this purpose, additional knowledge about the source or regularization is required. In this letter, we propose a novel two-stage strategy for multipolar source reconstruction from sub-sampled sparse data that takes advantage of the sparsity of the sources in the physical domain. The data at the Nyquist sampling rate is recovered from sub-sampled data and then a conventional inversion algorithm is used to reconstruct sources. The data recovery problem is linked to a spectrum recovery problem for the signal with the finite rate of innovations (FIR) that is solved using an annihilating filter-based structured Hankel matrix completion approach (ALOHA). For an accurate reconstruction, a Fourier inversion algorithm is used. The suitability of the approach is supported by experiments.

Annihilating filter-based structured Hankel matrix completion approach (ALOHA) , compressed sensing , inverse source problem , multipolar source , sparse data imaging

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Harbin Institute of Technology, School of Mathematics, Harbin, 150001, China
King Fahd University of Petroleum and Minerals, Department of Computer Engineering, College of Computing and Mathematics, Dhahran, 31261, Saudi Arabia
Nazarbayev University, Department of Mathematics, Astana, 010000, Kazakhstan

Harbin Institute of Technology
King Fahd University of Petroleum and Minerals
Nazarbayev University

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