An algorithm for linear programming which requires O(((m+n)n2+(m+n)1.5n)L) arithmetic operations
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Graphical models for machine learning and digital communication
Graphical models for machine learning and digital communication
A revolution: belief propagation in graphs with cycles
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Loopy Belief Propagation: Convergence and Effects of Message Errors
The Journal of Machine Learning Research
Distributed sparse random projections for refinable approximation
Proceedings of the 6th international conference on Information processing in sensor networks
Bayesian approach to best basis selection
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 05
Compressed sensing and Bayesian experimental design
Proceedings of the 25th international conference on Machine learning
Exploiting structure in wavelet-based Bayesian compressive sensing
IEEE Transactions on Signal Processing
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
A single-letter characterization of optimal noisy compressed sensing
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Combinatorial algorithms for compressed sensing
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Wavelet-based statistical signal processing using hidden Markovmodels
IEEE Transactions on Signal Processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
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
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A digital fountain approach to asynchronous reliable multicast
IEEE Journal on Selected Areas in Communications
Multiuser Detection of Sparsely Spread CDMA
IEEE Journal on Selected Areas in Communications
A single-letter characterization of optimal noisy compressed sensing
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
A low density lattice decoder via non-parametric belief propagation
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Nonparametric belief propagation
Communications of the ACM
Randomization of data acquisition and l1-optimization (recognition with compression)
Automation and Remote Control
Compressed sensing of astronomical images: orthogonal wavelets domains
Proceedings of the 12th International Conference on Computer Systems and Technologies
Seamless rate adaptation for wireless networking
Proceedings of the 14th ACM international conference on Modeling, analysis and simulation of wireless and mobile systems
Distributed video coding with compressive measurements
MM '11 Proceedings of the 19th ACM international conference on Multimedia
Compressed sensing construction of spectrum map for routing in cognitive radio networks
Wireless Communications & Mobile Computing
Sketching via hashing: from heavy hitters to compressed sensing to sparse fourier transform
Proceedings of the 32nd symposium on Principles of database systems
| Hi-index | 35.70 |
Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform asymptotically optimal Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length-N signal containing K large coefficients, our CS-BP decoding algorithm uses O (K log(N))measurements and O(N log2(N)) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models.