Bayesian Compressive Sensing Using Laplace Priors

Generative model for Compressive Sensing utilizing hiearchical Laplace priors

In our work, we formulate the CS reconstruction problem from a Bayesian perspective. We utilize a Bayesian model for the CS problem and propose the use of Laplace priors on the basis coefficients in a hierarchical manner. Our formulation includes the relevance vector machine (RVM) formulation as a special case, but results in smaller reconstruction errors while imposing sparsity to a higher extent. Moreover, we provide an alternative Bayesian inference procedure which results in an efficient greedy constructive algorithm. Our formulation naturally incorporates the advantages of the Bayesian framework, such as providing posterior distributions rather than point estimates, and therefore, providing an estimate of the uncertainty in the reconstructions, which, for instance, can be used as a feedback mechanism for adapting the data acquisition process. Furthermore, the resulting algorithms are fully automated since all required model parameters are estimated along with the unknown signal coefficients. Experimental results demonstrate that despite being fully automated, the proposed algorithm provides competitive and even higher reconstruction performance than state-of-the-art methods.

Hierarchical form of the Laplace prior enforcing signal sparsity.

This work will appear in IEEE International Conf. on Acoustics, Speech, and Signal Processing (ICASSP’09) (available below Babacan:2009:524 ). The detailed technical description of the proposed model and algorithm as well as experimental results can be found in the journal paper which is going to appear in IEEE Transactions on Image Processing. It can be downloaded from below Babacan:9999:203 .

The MATLAB source code for this work can be downloaded from here, which is provided for academic and research purposes. It contains the core algorithm code for fast Bayesian Compressive Sensing using Laplace priors, and an example script to run it. The code has been tested on Linux, Windows and Mac platforms, and it should run without problems with MATLAB versions 7 and up. Please read the README file and the comments in the source files for more information.

Please send your questions/comments/suggestions to Derin Babacan.