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.

中文翻译：

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阿拉伯海压缩声速剖面估计

摘要 声速分布（SSP）估计需要对声场进行反演；然而，测量的声场是有限的。这种不确定的问题需要正则化以确保物理上现实的解决方案。压缩感知是一种用于寻找欠定线性系统的稀疏解的技术。与奈奎斯特理论相比，该方法利用信号稀疏性从较少的测量中恢复原始信号。在本文中，声压使用泰勒展开和参数化 SSP 的形状函数近似线性化。压力和形状函数之间的线性关系使压缩传感能够重建 SSP。这里，SSP 使用学习字典 (LD) 和经验正交函数 (EOF) 建模，并通过正交匹配追踪 (OMP) 重建。来自阿拉伯海（北纬 14-19°和东经 65-70°之间）的 ARGO 网格数据集的 LD 压缩 SSP 观测是使用 K-SVD 算法生成的。仿真结果表明，学习字典比经验正交函数更好地解释了 SSP 可变性，并且可以通过使用字典学习的压缩感知以相对较小的误差估计 SSP。