Dynamic Compressive Sensing of Time-Varying Signals Via Approximate Message Passing

In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the li...

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Veröffentlicht in:	IEEE transactions on signal processing Jg. 61; H. 21; S. 5270 - 5284
Hauptverfasser:	Ziniel, Justin, Schniter, Philip
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.11.2013 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Applied sciences Approximate message passing (AMP) Approximation Bayes methods Bayesian analysis belief propagation compressed sensing Correlation Detection Detection, estimation, filtering, equalization, prediction dynamic compressive sensing Dynamics Exact sciences and technology expectation-maximization algorithms Heuristic algorithms Inference algorithms Information, signal and communications theory Kalman ﬁlters Learning Markov processes Mathematical models Message passing Sampling, quantization Signal and communications theory Signal, noise statistical signal processing Telecommunications and information theory Time series analysis time-varying sparse signals Vectors Performance evaluation Parameter estimation State of the art belief propagation expectation-maximization algorithms Kalman filter Wireless telecommunication Signal estimation Frequency estimation Adaptive method Time variation Approximate message passing (AMP) Learning Credal approach Digital communication Dynamic model Oracle Kalman filters Mobile radiocommunication statistical signal processing Filtering Probabilistic approach time-varying sparse signals Computational complexity Message passing dynamic compressive sensing Distributed control Causality EM algorithm Compressed sensing
ISSN:	1053-587X, 1941-0476
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Zusammenfassung:	In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the literature, the ability to perform inference on high-dimensional problems in a computationally efficient manner remains elusive. In response, we propose a probabilistic dynamic CS signal model that captures both amplitude and support correlation structure, and describe an approximate message passing algorithm that performs soft signal estimation and support detection with a computational complexity that is linear in all problem dimensions. The algorithm, DCS-AMP, can perform either causal filtering or non-causal smoothing, and is capable of learning model parameters adaptively from the data through an expectation-maximization learning procedure. We provide numerical evidence that DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety of operating conditions. We further describe the result of applying DCS-AMP to two real dynamic CS datasets, as well as a frequency estimation task, to bolster our claim that DCS-AMP is capable of offering state-of-the-art performance and speed on real-world high-dimensional problems.
Bibliographie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2013.2273196