Multiresolution probability analysis of gray-scaled images

Abstract

Digitized images can be decomposed into a sum of images by use of a multiresolution wavelet expansion. Each image of the expansion can be analyzed with a parametric statistical model for the histogram associated with each expansion component. The statistical analysis of the individual expansion components is relatively simple, whereas the analysis of the original image is complicated. We show that the probability model for each expansion component can be approximated with a Laplace probability-density function for some important applications in digital mammography. An approach to random variable analysis based on the predominant low-frequency characteristics of the random fields provides theoretical support for the approximation. The theoretical framework of multiresolution analysis provides a natural extension for modeling many levels of image detail simultaneously for special cases. We demonstrate this with a noise field simulation and a mammographic application, where the expansion components are treated as independent random variables.