Bach, breasts, and power-law processes

Arthur E. Burgess

doi:10.1117/12.431178

26 June 2001 Bach, breasts, and power-law processes

Arthur E. Burgess

Proceedings Volume 4324, Medical Imaging 2001: Image Perception and Performance; (2001) https://doi.org/10.1117/12.431178
Event: Medical Imaging 2001, 2001, San Diego, CA, United States

Abstract

Both the natural and manmade worlds abound with processes that have power-law spectra of the form, P(f)equalsK/f^(beta ). Statistical properties of such processes are dramatically different from those of smoothed Gaussian random processes. There is an extreme concentration of spectral power at low frequencies and a unique correlation distance does not exist. In addition, processes that do not have a low frequency cutoff have infinite (undefined) variance for infinite data sets. The fact that mammographic structure has a power-law spectrum does not tell one a great deal about the underlying process that generated the structure. Many different processes can have the same second order statistics, example classes are: deterministic, stochastic, self-similar, self-affine, and chaotic. It will be necessary to develop or adapt a variety of analytical techniques to investigate the nature of mammographic statistics. Some examples of power-law processes will be described and some statistical properties of mammograms will be presented.

Citation Download Citation

Arthur E. Burgess "Bach, breasts, and power-law processes", Proc. SPIE 4324, Medical Imaging 2001: Image Perception and Performance, (26 June 2001); https://doi.org/10.1117/12.431178

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