Combination Complex-Valued Bayesian Compressive Sensing Method for Sparsity Constrained Deconvolution Beamforming

Abstract

Several deconvolution methods have been proposed to reduce the mainlobe width and sidelobe intensity of conventional beamforming results without increasing the array aperture; however, most of them cannot perform well in the face of coherent targets. Therefore, it is discerning to deconvolve the complex-valued beamforming result rather than the beamforming intensity. However, conventional deconvolution methods focus on the beam intensity, and only a few studies have investigated complex-valued deconvolution beamforming (CDB). Considering the sparse property of the targets in practice, the CDB can be converted to a complex-valued inverse compressive sensing problem and put into the Bayesian framework. To solve it efficiently, a complex-valued Relevance-Vector-Machine (RVM) tool is used to build the complex-valued Bayesian compressive sensing (C-BCS) method that has excellent performance in terms of recovery accuracy and operating speed. However, the C-BCS method is not stable for the CDB because the point spread function is a rank deficiency matrix. To overcome this problem, we propose the combination C-BCS method that combines the block-sparse and C-BCS methods to improve the performance of solving the CDB. The simulation results proved that the proposed method performed better than intensity-based deconvolution methods for the beamforming results generated by the coherent targets. A beamforming image of a pool scene captured by a narrowband forward-looking sonar system was adopted to test various deconvolution methods, and the proposed method exhibited superiority in sidelobe suppression.