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Iterative Design of Concentration Factors for Jump Detection

Viswanathan, Adityavikram and Gelb, Anne and Cochran, Douglas (2012) Iterative Design of Concentration Factors for Jump Detection. Journal of Scientific Computing, 51 (3). pp. 631-649. ISSN 0885-7474.

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The concentration method of edge detection was developed to compute the locations and values of jump discontinuities in a piecewise-analytic function from its first few Fourier series coefficients. The accuracy and characteristic features of the resulting jump approximation depend on Fourier space “filter” factors known as concentration factors. In this paper, we provide a flexible, iterative framework for the design of these factors. Previously devised concentration factors are shown to be the solutions of specific problem formulations within this new framework. We also provide sample formulations of the procedure applicable to the design of concentration factors for data with missing spectral bands. Several illustrative examples are used to demonstrate the capabilities of the method.

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Additional Information:© 2011 Springer Science+Business Media, LLC. Received: 2 December 2010; Revised: 18 July 2011; Accepted: 27 July 2011; Published online: 9 September 2011. This work was supported in part by National Science Foundation grants CNS 0324957, DMS 0510813 and FRG 0652833.
Funding AgencyGrant Number
NSFCNS 0324957
NSFDMS 0510813
NSFFRG 0652833
Subject Keywords:Jump detection; Concentration edge detection; Convex optimization
Issue or Number:3
Record Number:CaltechAUTHORS:20120529-085548228
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31669
Deposited By: Tony Diaz
Deposited On:06 Jun 2012 17:46
Last Modified:03 Oct 2019 03:53

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