Direction of arrival estimation by Perona & Malik regularized Richardson-Lucy deconvolution

The Richardson-Lucy (RL) deconvolution algorithm is widely used in underwater acoustic array signal processing for the direction of arrival estimation due to its robustness and high resolution. However, its performance deteriorates at low signal-to-noise ratio, which is caused by the ill-posed inverse problem. To improve the algorithm performance, this paper proposes to combine the RL algorithm with Perona & Malik regularizer. The Perona & Malik regularizer is used to constrain the solution space by making the beam sidelobes smoother and peaks in targets' area sharper, thus mitigating the problems of increased sidelobe levels and worse resolution. The performance of the proposed algorithm is compared with that of the conventional beamformer, original RL algorithm, and total variation regularized RL method with simulated and experimental data. The results show that, compared to the other three methods, the proposed algorithm can effectively reduce the beam width, improve the multi-target resolution, and achieve lower sidelobe levels at signal-to-noise ratio above -10 dB.