Multiresolution probability analysis of random fields

Multiresolution wavelet methods can be used to simplify the statistical analysis of highly correlated nonGaussian random fields. Specific illustrations are given with the use of high-resolution digital mammograms. Fields of this kind are often difficult to analyze with parametric statistical methods. The introduction of a wavelet expansion simplifies the problem and permits the parametric analysis. The raw image is decomposed, and each expansion component is analyzed separately. The analysis applies to the individual components rather than the raw field. A suitable choice of probability function for modeling the individual components follows from the degree of detail information contained in each expansion component. The method is facilitated by using a linear operator approach. This method leads to a family of probability functions suitable for the random-field modeling of mammograms. in the limiting case the family of probability functions approaches a normal distribution. Generalizations are given that suggest possible extensions to other types of digitized image. (C) 1989 Optical Society of America [S0740-3232(99)01201-6].