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Adaptive multiresolution analysis based on synchronization

Pesenson, Meyer Z. and Pesenson, Isaac Z. (2011) Adaptive multiresolution analysis based on synchronization. Physical Review E, 84 (4). Art. No. 045202. ISSN 1539-3755.

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We propose an adaptive multiscale approach to data analysis based on synchronization. The approach is nonlinear, data driven in the sense that it does not rely on a priori chosen basis, and automatically determines the data scale. Numerical results for one- and two-dimensional cases illustrate that the method works effectively for the usual modulated signals such as chirps, etc., as well as for more complicated data with multiple scales. The method extends straightforwardly to functions defined on weighted graphs and grids in high dimensions. Connections with some other recent approaches to multiscale analysis are briefly discussed.

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Additional Information:© 2011 American Physical Society. Received 14 June 2011; published 11 October 2011. M.P. would like to thank M. Desbrun and J. Tropp for the stimulating discussions and suggestions that helped to improve the paper. We thank the anonymous reviewers for constructive suggestions that helped to improve the presentation. This work was in part supported by the grant from NGA, NURI HM1582-08-1-0019, and the grant from AFOSR, MURI FA9550-09-1-0643.
Funding AgencyGrant Number
NGA NURIHM1582-08-1-0019
AFOSR MURIFA9550-09-1-0643
Issue or Number:4
Classification Code:PACS: 05.45.Xt, 07.05.Kf, 02.30.Mv, 07.05.Rm
Record Number:CaltechAUTHORS:20111122-081725292
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Official Citation:Adaptive multiresolution analysis based on synchronization Meyer Z. Pesenson and Isaac Z. Pesenson Published 11 October 2011 (5 pages) 045202
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27902
Deposited By: Ruth Sustaita
Deposited On:22 Nov 2011 16:35
Last Modified:03 Oct 2019 03:27

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