Model-Based Compressive Sensing

Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K ¿ N elements from an N -dimensional basis. Instead of taking periodic samples, CS measures inner products with M < N random vectors...

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Veröffentlicht in:	IEEE transactions on information theory Jg. 56; H. 4; S. 1982 - 2001
Hauptverfasser:	Baraniuk, R.G., Cevher, V., Duarte, M.F., Hegde, C.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.04.2010 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Applied sciences Block sparsity Compressibility compressive sensing Computer simulation Concrete Costs Detection Detection, estimation, filtering, equalization, prediction Exact sciences and technology Greedy algorithms Guidelines Image coding Information science Information theory Information, signal and communications theory Mathematical models Measurement standards Miscellaneous Optimization Recovery Robustness Sampling Sampling methods Sampling, quantization Sensors Signal and communications theory signal model Signal processing Signal, noise Simulation sparsity Sufficient conditions Telecommunications and information theory Transform coding union of subspaces wavelet tree signal model State of the art Isometry Subspace method wavelet tree Random vector sparsity Block sparsity Optimization Sufficient condition Signal restoration Algorithm performance union of subspaces Model theory Signal processing Greedy algorithm Numerical simulation Overexposure Signal reconstruction Robustness Sampling Localization compressive sensing
ISSN:	0018-9448, 1557-9654
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Beschreibung
Zusammenfassung:	Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K ¿ N elements from an N -dimensional basis. Instead of taking periodic samples, CS measures inner products with M < N random vectors and then recovers the signal via a sparsity-seeking optimization or greedy algorithm. Standard CS dictates that robust signal recovery is possible from M = O(K log(N/K)) measurements. It is possible to substantially decrease M without sacrificing robustness by leveraging more realistic signal models that go beyond simple sparsity and compressibility by including structural dependencies between the values and locations of the signal coefficients. This paper introduces a model-based CS theory that parallels the conventional theory and provides concrete guidelines on how to create model-based recovery algorithms with provable performance guarantees. A highlight is the introduction of a new class of structured compressible signals along with a new sufficient condition for robust structured compressible signal recovery that we dub the restricted amplification property, which is the natural counterpart to the restricted isometry property of conventional CS. Two examples integrate two relevant signal models-wavelet trees and block sparsity-into two state-of-the-art CS recovery algorithms and prove that they offer robust recovery from just M = O(K) measurements. Extensive numerical simulations demonstrate the validity and applicability of our new theory and algorithms.
Bibliographie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 ObjectType-Article-1 ObjectType-Feature-2
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2010.2040894