Sound Speed Profiles Inversion by Pressure Inverted Echo Sounder and Reconstruction on Product Graph

Pressure inverted echo sounder (PIES) is an ocean observation instrument which is anchored to the seabed and measures the vertical acoustic travel time (VATT). Gravest Empirical Mode (GEM) and Optimal Interpolation are used to inverse sound speed profiles (SSPs) and reconstruct sound speed field (SSF) with the data of PIES array. A vertical SSP can be regarded as a known observation in three-dimension SSF but in fact the number of these observations is very small that leads to a challenge for reconstruction of SSF. To circumvent such an issue, graph signal processing (GSP) is introduced in this paper. The SSF is modeled as a product graph that can be decomposed into two smaller factor graphs. In this way, the original search space on product graph is reduced into the union of two much smaller spaces so that more accurate reconstruction results of SSF can be obtained by observing only a small subset of vertices on product graph. Besides the underlying structure of product graph, the bandlimited characteristic in graph spectrum analysis is leveraged to reconstruct SSF. The numerical results show that our proposed method performs better and achieves lower root mean square error (RMSE) in reconstruction of SSF.