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

Abstract

University of South FloridaDepartment of RadiologyDigital Medical Imaging ProgramTampa, Florida 33612-4799E-mail: clarke@splinter.moffitt.usf.eduAbstract. The multiresolution wavelet expansion is used as a simplify-ing mechanism for the parametric analysis of complicated highly corre-lated random fields. A previously developed approximation method isapplied to simulated statistically self-similar random fields for furtherevaluation. This approach can be considered as a simplifying method forrandom variable transformations for some important applications. Theapproach overcomes many of the difficulties associated with predictingthe output field probability distribution function resulting from passing anon-Gaussian random process through a linear network. Here, the mul-tiresolution wavelet expansion can be considered as a linear network.The ideas are illustrated with three related simulated noise fields: a whitenoise input field distributed proportional to a zero order hyperbolic Besselfunction and two 1/f noise processes resulting from filtering the whitenoise process. The fields are analyzed with an orthogonal multiresolutionwavelet expansion. The expansion components are studied with para-metric analysis, where the probability models are all derived from onefamily of functions. In addition, the study illustrates some interesting non-intuitive statistical properties of the filtered fields.