Compressive Acoustic Sound Speed Profile Estimation in the Arabian Sea

Abstract

The sound speed profile (SSP) estimation requires the inversion of acoustic fields; however, the measured sound field is limited. Such an underdetermined problem requires regularization to ensure physically realistic solutions. Compressive sensing is a technique used to find sparse solutions of an underdetermined linear system. Compared with the Nyquist theory, this method uses the signal sparsity to restore the original signal from fewer measurements. In this paper, the acoustic pressure is approximately linearized using the Taylor expansion with the shape functions that parameterize the SSP. The linear relation between the pressure and the shape functions enables compressive sensing to reconstruct the SSP. Here, the SSPs are modeled using the learning dictionaries (LDs) and empirical orthogonal functions (EOFs) and reconstructed by the orthogonal matching pursuit (OMP). The LDs compressive SSP observations from the ARGO gridded data set in the Arabian Sea (between 14–19°N and 65–70°E) are generated using the K-SVD algorithm. Simulation results show that the learning dictionaries explain SSP variability better than the empirical orthogonal functions, and the SSPs can be estimated with a relatively small error by compressive sensing using dictionary learning.

Keywords:

• ARGO
• compressive sensing
• dictionary learning
• orthogonal matching pursuit
• sound speed profile

Acknowledgements

Authors acknowledge the Chinese Argo Project, and to all the research groups contributing to this activity. The Argo data were collected and made freely available by the Chinese Argo Project and the national programs that contribute to it (http://www.argo.org.cn/).

Appendix A

Table 1. The acronyms list.

Additional information

Funding

This work was supported by the National Key R&D Program of China under Grant number 2018YFC1405900; The National Natural Science Foundation of China under Grant number 11704225; State Key Laboratory of Acoustics of Chinese Academy of Sciences under Grant number SKLA201902; SDUST Research Fund under Grant number 2019TDJH103; and Talent introduction plan for Youth Innovation Team in universities of Shandong Province under Grant innovation team of satellite positioning and navigation.