Non-convex sparse beamformer

Area of Science:

• Signal Processing
• Array Signal Processing
• Computational Electromagnetics

Background:

• Sparse beamforming methods like LASSO and FL often underestimate source amplitudes due to l1-norm regularization's soft-thresholding effect.
• This amplitude underestimation is a significant limitation for accurately characterizing sources, especially extended ones.

Purpose of the Study:

• To introduce a novel set of non-convex regularizers (NCP) designed to mitigate amplitude bias in sparse beamforming.
• To develop and validate the non-convex fused least absolute shrinkage and selection operator (NFL) method that preserves sparsity and smoothness while improving amplitude recovery.

Main Methods:

• Integration of non-convex penalties (NCP) into the fused least absolute shrinkage and selection operator (FL) framework to create the NFL model.
• Utilizing the proximal operator for efficient handling of non-convex penalties.
• Solving the NFL model using the alternating direction method of multipliers (ADMM).

Main Results:

• The proposed NFL method effectively reduces shrinkage on large coefficients, leading to more accurate source amplitude estimation.
• Demonstrated improvement in amplitude recovery for both point and extended sources compared to existing sparse beamforming techniques.
• The NFL method successfully preserves the desired sparsity and smoothness of the source profile.

Conclusions:

• The developed non-convex fused least absolute shrinkage and selection operator (NFL) offers a significant advancement in sparse beamforming.
• This method overcomes the amplitude underestimation problem inherent in traditional l1-norm-based sparse beamforming techniques.
• NFL provides a robust solution for accurate source amplitude estimation in various scenarios, including extended sources.