MATLAB Source Code for Bayesian Compressive Sensing

This article explores Bayesian methodology and its application in compressive sensing. Bayesian inference is a statistical approach for estimating unknown parameters, while Bayesian compressive sensing leverages Bayesian principles for signal reconstruction from limited measurements. The provided MATLAB source code implements key algorithms including:

- Bayesian sparse signal recovery using relevance vector machines (RVM)
- Hierarchical Bayesian models for automatic parameter estimation
- Markov Chain Monte Carlo (MCMC) sampling techniques
- Signal reconstruction with uncertainty quantification

The code features implementation of prior distributions (Gaussian, Laplace), evidence maximization, and iterative optimization procedures. Main functions include Bayesian basis pursuit, parameter learning via expectation-maximization, and posterior probability calculations. The implementation supports both 1D and 2D signal processing with configurable sparsity parameters and noise models.