Two-Dimensional Pattern-Coupled Sparse Bayesian Learning via Generalized Approximate Message Passing.

Area of Science:

• Signal Processing
• Machine Learning
• Computational Imaging

Background:

• 2D block-sparse signals are common in applications like radar imaging and foreground detection.
• Recovering these signals is challenging due to unknown, irregular cluster patterns.
• Existing methods often require prior knowledge of signal structure.

Purpose of the Study:

• To develop a novel method for recovering 2D block-sparse signals with unknown cluster patterns.
• To automatically learn irregular block structures without prior partitioning information.
• To improve signal recovery performance and reduce computational complexity.

Main Methods:

• A 2D pattern-coupled hierarchical Gaussian prior model is proposed.
• A soft coupling mechanism among coefficients is implemented via shared hyperparameters.
• A computationally efficient Bayesian inference method integrating generalized approximate message passing (GAMP) is developed.

Main Results:

• The proposed method effectively learns underlying irregular cluster patterns.
• Competitive recovery performance is demonstrated across various 2D sparse signal recovery tasks.
• Significant reduction in computational complexity compared to existing methods is achieved.

Conclusions:

• The developed Bayesian inference method accurately recovers 2D block-sparse signals with unknown patterns.
• The pattern-coupled hierarchical Gaussian prior model enables robust and efficient signal recovery.
• This approach advances signal processing and image reconstruction techniques.