Multiresolution analysis of two-dimensional 1/f processes: approximation methods for random variable transformations

John J. Heine; Stanley R. Deans; Deepak Gangadharan; Laurence P. Clarke

doi:10.1117/1.602201

1 September 1999 Multiresolution analysis of two-dimensional 1/f processes: approximation methods for random variable transformations

John J. Heine, Stanley R. Deans, Deepak Gangadharan, Laurence P. Clarke

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Optical Engineering, Vol. 38, Issue 9, (September 1999). https://doi.org/10.1117/1.602201

The multiresolution wavelet expansion is used as a simplifying mechanism for the parametric analysis of complicated highly correlated random fields. A previously developed approximation method is applied to simulated statistically self-similar random fields for further evaluation. This approach can be considered as a simplifying method for random variable transformations for some important applications. The approach overcomes many of the difficulties associated with predicting the output field probability distribution function resulting from passing a non-Gaussian random process through a linear network. Here, the multiresolution wavelet expansion can be considered as a linear network. The ideas are illustrated with three related simulated noise fields: a white noise input field distributed proportional to a zero order hyperbolic Bessel function and two 1/f noise processes resulting from filtering the white noise process. The fields are analyzed with an orthogonal multiresolution wavelet expansion. The expansion components are studied with parametric analysis, where the probability models are all derived from one family of functions. In addition, the study illustrates some interesting nonintuitive statistical properties of the filtered fields.

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John J. Heine, Stanley R. Deans, Deepak Gangadharan, and Laurence P. Clarke "Multiresolution analysis of two-dimensional 1/f processes: approximation methods for random variable transformations," Optical Engineering 38(9), (1 September 1999). https://doi.org/10.1117/1.602201

Published: 1 September 1999

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