Compressive sensing via nonlocal low-rank regularization.

Area of Science:

• Signal Processing
• Image Reconstruction
• Compressed Sensing

Background:

• Sparsity is crucial for signal reconstruction from limited measurements.
• Structured or group sparsity offers improved performance in compressed sensing (CS).

Purpose of the Study:

• To propose and evaluate a nonlocal low-rank regularization (NLR) approach for exploiting structured sparsity in CS.
• To apply the NLR method to photographic and MRI image reconstruction.
• To introduce a nonconvex surrogate function for rank optimization in CS.

Main Methods:

• Developed a nonlocal low-rank regularization (NLR) framework.
• Employed a nonconvex log det(X) as a surrogate for rank, instead of the nuclear norm.
• Implemented a fast algorithm using the alternative direction multiplier method (ADMM).

Main Results:

• The proposed NLR-CS algorithm demonstrated superior performance compared to existing CS methods.
• Extensive experiments validated the benefits of the nonconvex surrogate function.
• The ADMM-based implementation significantly improved computational efficiency.

Conclusions:

• The NLR-CS approach effectively leverages structured sparsity for enhanced image reconstruction.
• Nonconvex regularization offers advantages over convex methods for rank approximation in CS.
• The developed algorithm provides a computationally efficient and high-performing solution for CS image recovery.