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Abstract:
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Many measured biomedical signals are inherently noisy and, as a rule, the noise carries relevant diagnostic information. In some extreme cases, for example in the analysis of high frequency pupil diameter measurements, the trends in the measured time series depend on the ambient light and are irrelevant for assessing potential visual imparity -- all information is contained in the noise. In this overview talk we discuss statistical inference based on descriptors/summaries distilled form the noisy biomedical data. The signals and images in biometric analysis often exhibit self-similarity and are well modeled by (multi) fractional Brownian motions/fields. A range of fractal and multifractal indices derived form the spectral characteristics of the measurements proved useful in disease diagnostic tasks, and often represent a testing modality independent of the traditionally used modalities. In the talk we discuss the use and performance of various multiscale spectral measures, their robust counterparts, wavelet-based multifractal indices, and dual wavelet spectra. The methods are illustrated by real-life measurements in the area of diagnostics of breast and ovarian cancers.
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