Probability-Based Complex-Valued Fast Iterative Shrinkage-Thresholding Algorithm for Deconvolution Beamforming

Conventional beamforming is widely used in sonars and radars owing to its robustness and low complexity; however, it suffers from low beam resolution and high-intensity sidelobes. Various imaging deblurring methods have been used in deconvolution beamforming to improve the beam resolution. A considerable limitation of these intensity-based methods is that the real-valued model mismatches the signals in practice and ignores the coherent information of the received signals. This study proposes a probability-based complex-valued fast iterative shrinkage-thresholding algorithm (CFISTA) to extend deconvolution beamforming to the complex domain. In this novel algorithm, the complex gradient descent and complex probability mapping are combined. Fast Fourier transform acceleration and clustering prior constraints are used on the targets to improve the efficiency and accuracy of the model. Simulation results of planar arrays show that the proposed method has superior beam resolution, sidelobe suppression, running time, and noise immunity compared with those of intensity-based methods.