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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| Published in: | IEEE transactions on signal processing Vol. 61; no. 19; pp. 4658 - 4672 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York, NY
IEEE
01.10.2013
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects: | |
| ISSN: | 1053-587X, 1941-0476 |
| Online Access: | Get full 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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| 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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