NDLI: On the Relation Between Sparse Reconstruction and Parameter Estimation With Model Order Selection

Content Provider	IEEE Xplore Digital Library
Author	Austin, C.D. Moses, R.L. Ash, J.N. Ertin, E.
Copyright Year	2007
Abstract	We examine the relationship between sparse linear reconstruction and the classic problem of continuous parametric modeling. In sparse reconstruction, one wishes to recover a sparse amplitude vector from a measurement that is described as a linear combination of a small number of discrete additive components. Recent results in the compressive sensing literature have provided fast sparse reconstruction algorithms with guaranteed performance bounds for problems with certain structure. In this paper, we show an explicit connection between sparse reconstruction and parameter/order estimation and demonstrate how sparse reconstruction may be used to solve model order selection and parameter estimation problems. The structural assumption used in compressive sensing to guarantee reconstruction performance-the Restricted Isometry Property-is not satisfied in the general parameter estimation context. Nonetheless, we develop a method for selecting sparsity parameters such that sparse reconstruction mimics classic order selection criteria such as Akaike information criterion (AIC) and Bayesian information criterion (BIC). We compare the performance of the sparse reconstruction approach with traditional model order selection/parameter estimation techniques for a sinusoids-in-noise example. We find that the two methods have comparable performance in most cases, and that sparse linear modeling performs better than traditional model-based parameter/order estimation for closely spaced sinusoids with low signal-to-noise ratio.
Sponsorship	IEEE Signal Processing Society
Starting Page	560
Ending Page	570
Page Count	11
File Size	954069
File Format	PDF
ISSN	19324553
Volume Number	4
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Parameter estimation Image reconstruction Parametric statistics Vectors Reconstruction algorithms Sampling methods Direction of arrival estimation Noise measurement Linear systems Sparse matrices sparse reconstruction Compressed sensing (CS) information criteria model order selection parameter estimation
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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