Probing the Pareto Frontier for Basis Pursuit Solutions
SIAM Journal on Scientific Computing
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Beamforming is a process that supplies directional gain to sensor array processing. One modality where beamforming adds great value is passive sonar, where real-aperture arrays receive signals emitted by acoustic sources. In passive sonar systems, the beamformer is the backbone of a processing structure that detects, localizes, and classifies external targets. Conventional beamformers use deterministic time-delays (often implemented as phase shifts) to arrange coherent addition of plane-wave signals at each sensor. Recently, adaptive beamformers take advantage of signal time history by imposing a model on the environment. Basis Pursuit is another reconstruction approach used in Compressed Sensing that also enforces a physics-based model - in this case a model of scene sparsity. This paper describes an application of this technique to the beamforming problem. The main benefit of the Basis Pursuit beamforming approach is that it is robust to missing array elements, providing nearly full-aperture performance in a reduced sensor environment. This result is advantageous in the case of processing with inoperative hydrophones. It may also provide cost savings by allowing array design with fewer hydrophones.