Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Variational Relevance Vector Machines
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Convex Optimization
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Bayesian compressive sensing and projection optimization
Proceedings of the 24th international conference on Machine learning
Nonparametric belief propagation
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Linear Regression With a Sparse Parameter Vector
IEEE Transactions on Signal Processing
Sparse Bayesian learning for basis selection
IEEE Transactions on Signal Processing
An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem
IEEE Transactions on Signal Processing - Part II
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Constructing free-energy approximations and generalized belief propagation algorithms
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Sufficient Conditions for Convergence of the Sum–Product Algorithm
IEEE Transactions on Information Theory
On Binary Probing Signals and Instrumental Variables Receivers for Radar
IEEE Transactions on Information Theory
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We present a belief propagation (BP)-based sparse Bayesian learning (SBL) algorithm, referred to as the BP-SBL, to recover sparse transform coefficients in large scale compressed sensing problems. BP-SBL is based on a widely used hierarchical Bayesian model, which is turned into a factor graph so that BP can be applied to achieve computational efficiency. We prove that the messages in BP are Gaussian probability density functions and therefore, we only need to update their means and variances when we update the messages. The computational complexity of BP-SBL is proportional to the number of transform coefficients, allowing the algorithms to deal with large scale compressed sensing problems efficiently. Numerical examples are provided to demonstrate the effectiveness of BP-SBL.