Variational Bayesian Compressed Sensing

An extension of the variational relevance vector machine (VRVM) for highly scalable sparse Bayesian learning in compressed sensing recovery problems.

Note: This repository is woefully out of date. For peer-reviewed code, please see sbl-sandbox.

Introduction

Compressed sensing deals with the recovery of signals from incomplete measurements, using knowledge of the signal structure in some other domain (e.g. frequency, wavelet, etc.). While recovery problems in compressed sensing have been analyzed from the perspective of Bayesian inference, most of the resulting algorithms do not yield fully Bayesian estimates, and fully Bayesian approaches scale poorly.

The variational Bayesian compressed sensing (VBCS) algorithm extends the VRVM to bring the computational requirements of fully Bayesian estimation (or rather its variational approximation) down to levels that enable modeling of large problem instances.

Source code

The main source code of vbcs is stored in sources, where implementations of both VBCS and the VRVM are provided.

Example problems

Numerical problems demonstrating the features of vbcs are stored in subdirectories of examples.

Figures

Scripts for generating the figures in the vbcs publication are stored in subdirectories of figures.

Licensing

The vbcs sources and example files released under the MIT license. See the LICENSE.md file for the complete license terms.