Hierarchical Bayesian Approach For Jointly-Sparse Solution Of Multiple-Measurement Vectors

Area of Science:

• Signal Processing
• Statistical Modeling
• Machine Learning

Background:

• Estimating signals with few active components (sparse signals) is crucial in various scientific fields.
• Existing methods like Orthogonal Matching Pursuit (OMP) struggle with complex sparse structures.
• Multiple Measurement Vectors (MMVs) present challenges due to their jointly sparse nature.

Purpose of the Study:

• To develop an advanced statistical model for signal recovery from Multiple Measurement Vectors (MMVs).
• To address the specific challenge of jointly sparse and block sparse structures in signal representations.
• To offer a superior alternative to existing greedy algorithms for sparse signal estimation.

Main Methods:

• Proposed a hierarchical Bayesian model to capture jointly sparse structures in MMVs.
• Extended the model to incorporate block sparsity, representing clumps of neighboring supports.
• Evaluated the model's performance against OMP and a modified OMP algorithm through examples.

Main Results:

• The hierarchical Bayesian model effectively handles MMVs with both joint sparsity and block sparsity.
• Demonstrated superior performance of the proposed model compared to OMP and its variants.
• The model accurately estimates signals with complex sparse structures.

Conclusions:

• Hierarchical Bayesian modeling provides a powerful framework for sparse signal recovery in MMVs.
• The proposed model offers improved accuracy and robustness for signals with joint and block sparsity.
• This approach advances sparse representation techniques in signal processing.