| Sensitivity analysis of solutions of the harmonic inversion problem: are all data points created equal? | |
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MedLine Citation:
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PMID: 20663693 Owner: NLM Status: MEDLINE |
Abstract/OtherAbstract:
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We consider the harmonic inversion problem, and the associated spectral estimation problem, both of which are key numerical problems in NMR data analysis. Under certain conditions (in particular, in exact arithmetic) these problems have unique solutions. Therefore, these solutions must not depend on the inversion algorithm, as long as it is exact in principle. In this paper, we are not concerned with the algorithmic aspects of harmonic inversion, but rather with the sensitivity of the solutions of the problem to perturbations of the time-domain data. A sensitivity analysis was performed and the counterintuitive results call into question the common assumption made in "super-resolution" methods using non-uniform data sampling, namely, that the data should be sampled more often where the time signal has the largest signal-to-noise ratio. The numerical analysis herein demonstrates that the spectral parameters (such as the peak positions and amplitudes) resulting from the solution of the harmonic inversion problem are least susceptible to the perturbations in the values of data points at the edges of the time interval and most susceptible to the perturbations in the values at intermediate times. |
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Authors:
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Hasan Celik; A J Shaka; V A Mandelshtam |
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Publication Detail:
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Type: Journal Article; Research Support, U.S. Gov't, Non-P.H.S. Date: 2010-06-30 |
Journal Detail:
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Title: Journal of magnetic resonance (San Diego, Calif. : 1997) Volume: 206 ISSN: 1096-0856 ISO Abbreviation: J. Magn. Reson. Publication Date: 2010 Sep |
Date Detail:
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Created Date: 2010-08-23 Completed Date: 2010-12-08 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 9707935 Medline TA: J Magn Reson Country: United States |
Other Details:
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Languages: eng Pagination: 120-6 Citation Subset: IM |
Copyright Information:
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(c) 2010. Published by Elsevier Inc. |
Affiliation:
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Department of Chemistry, University of California, Irvine, CA 92697-2025, USA. hcelik@uci.edu |
Export Citation:
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| MeSH Terms | |
Descriptor/Qualifier:
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Algorithms* Analog-Digital Conversion Data Interpretation, Statistical Linear Models Magnetic Resonance Spectroscopy / statistics & numerical data* |
From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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