Multiresolution analysis using adaptive wavelets

J. Glynn Jones; Graham H. Watson

doi:10.1117/12.170016

15 March 1994 Multiresolution analysis using adaptive wavelets

J. Glynn Jones, Graham H. Watson

Proceedings Volume 2242, Wavelet Applications; (1994) https://doi.org/10.1117/12.170016
Event: SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, 1994, Orlando, FL, United States

Abstract

A form of nonlinear multiresolution analysis is described in which, by appropriate scaling and choice of analyzing wavelet, information concerning the structure of a signal or image is derived from local maxima and minima in the data transformed to position-scale, or wavelet, space. There results a data coding as a discrete sum of 'signal wavelets' that are generated adaptively to give a good local fit to the data, rather than being specified a priori as in standard applications of the wavelet transform. Although the wavelets generated in this manner are not in general mutually orthogonal, an orthogonal set of basis functions is derived subsequently in the form of linear combinations of appropriately weighted wavelets. A further novel aspect of the method is the introduction of a non-Gaussian statistical model which is fitted to the data and used to categorize individual data samples and to focus attention upon unusual events. Statistical distributions at different scales are related by means of fractal exponents. Applications are described to remote- sensing imagery, where the 'unusual events' are typically man- made artifacts in natural environmental backgrounds, and to a medically oriented signal in the form of heart rate, where the method can be used to draw attention to unusual patterns of heart beats.

Citation Download Citation

J. Glynn Jones and Graham H. Watson "Multiresolution analysis using adaptive wavelets", Proc. SPIE 2242, Wavelet Applications, (15 March 1994); https://doi.org/10.1117/12.170016

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