Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and...

Area of Science:

• Signal Processing
• Machine Learning
• Statistical Inference

Background:

• Compressive sensing enables efficient signal acquisition and reconstruction of sparse signals.
• Sparse Bayesian learning (SBL) methods, enhanced by variational Bayesian (VB) inference, offer efficient solutions for compressive sensing inverse problems.
• Bernoulli-Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) are common priors for modeling sparse signals.

Purpose of the Study:

• To compare the performance of BGiG and GiG models for sparse signal recovery under VB inference.
• To address the lack of comprehensive comparison between BGiG and GiG models in VB inference for unstructured sparse signals.
• To identify potential signal reconstruction issues and suggest performance improvements for each model.

Main Methods:

• Utilizing compressive sensing (CS) for sub-Nyquist sampling.
• Applying variational Bayesian (VB) inference within the sparse Bayesian learning (SBL) framework.
• Modeling sparse signals using BGiG and GiG Bayesian priors.

Main Results:

• Detailed analysis of BGiG and GiG model performance under VB inference for sparse signal recovery.
• Identification of specific signal reconstruction challenges associated with each model.
• Comparative evaluation of the two models in the absence of predefined signal structures.

Conclusions:

• The study provides a comprehensive comparison of BGiG and GiG models within the VB inference framework for compressive sensing.
• Insights are offered into the strengths and weaknesses of each model for sparse signal recovery.
• Recommendations are proposed for enhancing the performance of BGiG and GiG models in practical applications.