Iterative Design of Concentration Factors for Jump Detection

Authors:
Adityavikram Viswanathan;Anne Gelb;Douglas Cochran
Affiliations:
Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, USA 91125;School of Mathematical and Statistical Sciences, Arizona State University, Tempe, USA 85287-1804;School of Electrical, Computer & Energy Engineering, Arizona State University, Tempe, USA 85287-5706
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

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.