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