Compressive sensing or sparse coding is to learn sparse representation of data. The simplest method is to use linear regression with L1 regularization. While this package provides Bayesian treatment for sparse coding problems.
The sparse coding problem is modeled as linear regression with a sparse prior (automatic relevance determination, ARD), which is also known as Relevance Vector Machine (RVM). The advantage is that it can do model selection automatically. As a result, this is no need to mannully specify the regularization parameter (learned from data) and better sparse recovery can be obtained. Please run the demo script in the package to give it a try.
This package is now a part of the PRML toolbox (http://www.mathworks.com/matlabcentral/fileexchange/55826-pattern-recognition-and-machine-learning-toolbox).