Non-convex sparse beamformer

Sparse beamforming techniques, such as least absolute shrinkage and selection operator (LASSO) and fused least absolute shrinkage and selection operator (FL), underestimate source amplitude due to the soft-thresholding effect of the l1-norm regularization. For sparse beamforming, a new set of non-convex regularizers is introduced. They are designed to accurately recover source amplitudes—including those of extended sources—by reducing the shrinkage imposed on large coefficients. Integrating these non-convex penalties (NCP) within the FL framework, we propose the non-convex fused least absolute shrinkage and selection operator (NFL) that avoids amplitude bias while preserving sparsity and smoothness of the source profile. The NFL model leverages the proximal operator for handling NCP and is solved using the alternating direction method of multipliers. Several examples demonstrate that the proposed method improves amplitude estimation for both point and extended sources.