Compressed Sensing of Underwater Acoustic Signals via Structured Approximation l₀-Norm

The underwater wireless sensor networks enable the telemonitoring and communications technologies of underwater information play important roles in the gathering process of scientific data in collaborative monitoring missions. However, to design such a system, several aspects must be considered to make fewer resources required, such as energy efficiency, miniaturization, the required functionality, etc. Conventional methods of data compression and reconstruction fail in energy efficiency. Different from the conventional compression methods, compressive sampling (CS) provides a new perspective to compress huge data with low energy consumption. Unfortunately, the recordings of underwater acoustic signal (UAS) are nonsparse in time domain. Hence, the current CS methods cannot be used directly for compression and reconstruction of UAS. This study adopts the wavelet-Transform-based dictionary matrix to build a framework for sparse representation; then, introduces an approach based on structured approximation $l-0$ (SAL0) norm, which is designed by exploring and exploiting the correlation structure of UAS. The proposed method searches the optimal sparse solution via steepest descent method and then projects the solution to its feasible set. Combing with the compression matrix and dictionary matrix, the estimation of SAL0 method is used for reconstructing nonsparse UAS.