部分范数约束的稀疏恢复算法及其在单载波水声数据遥测中的应用

Partial-norm-constrained sparse recovery algorithm and its application on single carrier underwater-acoustic-data telemetry

对于单载波水声数据压缩与恢复问题,压缩感知能以较低能耗获得信号压缩与恢复效果。但压缩感知核心目标是直接求最小l_0范数,该问题表现为NP难问题,因此,常将其转化为求l_1范数约束最小化问题,而求l_1范数约束最小化的稀疏解精度有限。基于此,推导出基于部分范数约束的稀疏信号恢复算法,该算法通过部分范数约束在拉格朗日求解中增加一个零吸引项,从而动态分配稀疏抽头的软阈值。同时,该算法用于实际海上数据的遥测,结合离散余弦变换(DCT),可将单载波水声数据恢复精度提高。

To solve the problem of single carrier underwater-acoustic-data telemetry, compressive sensing（CS） provides competitive performance of compression and recovery with low energy consumption. The primary objective of CS is to minimize the l0 norm, which is an NP hard problem. Hence, the common methods were transferred to minimize l1 norm. However, l1 norm minimization provided a limited accuracy. A partial-norm-constraint（PNC） based sparse signal recovery method was derived, which adopted PNC as a zero attraction in a Lagrange method, to distribute the soft threshold for the non-zero taps. The proposed method is used for at-sea data telemetry. Combining with DCT, the proposed method improves the recovery accuracy.