Expectation-Maximization Gaussian-Mixture Approximate Message Passing
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 m...
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| Vydané v: | IEEE transactions on signal processing Ročník 61; číslo 19; s. 4658 - 4672 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York, NY
IEEE
01.10.2013
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Predmet: | |
| ISSN: | 1053-587X, 1941-0476 |
| On-line prístup: | Získať plný text |
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| 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. |
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| AbstractList | 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. |
| Author | Schniter, Philip Vila, Jeremy P. |
| Author_xml | – sequence: 1 givenname: Jeremy P. surname: Vila fullname: Vila, Jeremy P. email: vila.2@osu.edu organization: Dept. of Electr. & Comput. Eng., Ohio State Univ., Columbus, OH, USA – sequence: 2 givenname: Philip surname: Schniter fullname: Schniter, Philip email: schniter@ece.osu.edu organization: Dept. of Electr. & Comput. Eng., Ohio State Univ., Columbus, OH, USA |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=27783901$$DView record in Pascal Francis |
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| References | ref13 ref12 ref36 ref14 ref31 ref30 ref33 ref11 ref32 ref10 (ref37) 0 ref2 zhang (ref34) 2011 dempster (ref15) 1977; 39 ref17 ref16 cevher (ref35) 2009 ref19 ref18 vila (ref1) 2011 neal (ref23) 1999 bishop (ref24) 2007 buldygin (ref28) 2000 ref26 ref25 ref22 ref21 ref27 kamilov (ref20) 2012 ref29 ref8 ref7 ref9 ref4 ref3 ref5 tibshirani (ref6) 1996; 58 |
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| SubjectTerms | Algorithms Applied sciences Approximation Approximation algorithms belief propagation Complexity theory Compressed sensing Detection, estimation, filtering, equalization, prediction Exact sciences and technology expectation maximization algorithms Gaussian mixture model Information, signal and communications theory Mathematical models Maximization Message passing Noise Noise measurement Reconstruction Recovery Run time (computers) Sampling, quantization Sensors Signal and communications theory Signal, noise Telecommunications and information theory Vectors |
| Title | Expectation-Maximization Gaussian-Mixture Approximate Message Passing |
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