Name
Abstract | ||
|---|---|---|
When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal's non-zero coefficients can have a profound effect on recovery mean-squared error (MSE). If this distribution was a priori known, then one could use computationally efficient approximate message passing (AMP) techniques for nearly minimum MSE (MMSE) recovery. In practice, however, the distribution is unknown, motivating the use of robust algorithms like LASSO—which is nearly minimax optimal—at the cost of significantly larger MSE for non-least-favorable distributions. As an alternative, we propose an empirical-Bayesian technique that simultaneously learns the signal distribution while MMSE-recovering the signal—according to the learned distribution—using AMP. In particular, we model the non-zero distribution as a Gaussian mixture and learn its parameters through expectation maximization, using AMP to implement the expectation step. Numerical experiments on a wide range of signal classes confirm the state-of-the-art performance of our approach, in both reconstruction error and runtime, in the high-dimensional regime, for most (but not all) sensing operators. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/TSP.2013.2272287 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
gaussian distribution,mean square error methods,message passing,minimax techniques,signal processing,lasso,mmse recovery,empirical-bayesian technique,expectation maximization,expectation-maximization gaussian-mixture approximate message passing,high-dimensional regime,mean-squared error,minimax optimal,noisy compressive linear measurements,nonleast-favorable distributions,signal distribution,signal non-zero coefficients,sparse signal recovery,compressed sensing,gaussian mixture model,belief propagation,expectation maximization algorithms | Signal processing,Minimax,Mathematical optimization,Expectation–maximization algorithm,A priori and a posteriori,Gaussian,Operator (computer programming),Mathematics,Mixture model,Message passing | Journal |
Volume | Issue | ISSN |
61 | 19 | 1053-587X |
Citations | PageRank | References |
56 | 1.85 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jeremy P. Vila | 1 | 106 | 4.38 |
| Philip Schniter | 2 | 1620 | 93.74 |