Compressed Sensing via Sequential Majorization-Minimization and Collaborative Neurodynamic Optimization

Area of Science:

• Signal Processing
• Optimization
• Applied Mathematics

Background:

• Compressed sensing (CS) formulations using the $\ell _{0}$-norm objective are computationally challenging due to nonconvexity and discontinuity.
• Minimizing power-mean functions with large negative exponents in CS can lead to numerical instability.

Purpose of the Study:

• To develop a robust global optimization method for compressed sensing problems.
• To address the numerical instability and anchor point dependency issues in $\ell _{0}$-norm minimization.

Main Methods:

• Formulation of a global optimization problem using a power-mean function for compressed sensing.
• Reformulation as a sequential majorization-minimization (MM) problem with iteratively reweighted convex surrogates.
• Employment of multiple neurodynamic optimization models with particle swarm optimization for collaborative global solution seeking.

Main Results:

• The proposed method demonstrates superior performance in signal sparsity and reconstruction accuracy.
• Outperforms 14 state-of-the-art algorithms in experimental evaluations.
• Mitigates numerical instability and reduces dependency on initial anchor points.

Conclusions:

• The novel approach provides an effective and stable solution for compressed sensing.
• Achieves enhanced signal recovery and sparsity, advancing the field of signal processing.