  A number of approaches have dealt with statistical assessment of
self-similarity, and many of those are based on multiscale concepts. Most rely
on certain distributional assumptions which are usually violated by real data
traces, often characterized by large temporal or spatial mean level shifts,
missing values or extreme observations. A novel, robust approach based on
Theil-type weighted regression is proposed for estimating self-similarity in
two-dimensional data (images). The method is compared to two traditional
estimation techniques that use wavelet decompositions; ordinary least squares
(OLS) and Abry-Veitch bias correcting estimator (AV). As an application, the
suitability of the self-similarity estimate resulting from the the robust
approach is illustrated as a predictive feature in the classification of
digitized mammogram images as cancerous or non-cancerous. The diagnostic
employed here is based on the properties of image backgrounds, which is
typically an unused modality in breast cancer screening. Classification results
show nearly 68% accuracy, varying slightly with the choice of wavelet basis,
and the range of multiresolution levels used.
