Adaptive Compressive Beamforming Based on Bi-Sparse Dictionary Learning

Dictionary learning (DL) methods are commonly employed in feature extraction, image inpainting, and denoising. Appealing to the adaptive sparse representation of DL, a generalized DL framework is devised in this work, through which any DL approach can be applied straightforwardly to a linear model, e.g., the beamforming model employed here. Specifically, to exploit the adaptation of DL and make the most use of the prior information, a bi-sparse dictionary learning (BSDL)-based beamforming model is proposed, which is composed of multiple basis dictionaries in analysis form and trained dictionaries in synthesis form. The alternating direction method of multipliers (ADMM) and the block proximal gradient (BPG) method are employed to solve the problem. With the proposed bi-sparse representation structure, matrix inversion operation can be performed beforehand, and a scaling rule is designed to select the tuning parameters adaptively and iteratively. As demonstrated by the simulation and experiment results, the BSDL-based beamforming approach is superior to the other state-of-the-art beamforming methods in terms of recovery accuracy and retaining competitive uncertainty, even without basis dictionaries.