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.