Multi-Scale Methods Applied to Small-Angle X-Ray Scattering Images of Breast Tumour Tissue

Abstract

This thesis develops statistical methods for investigating small angle x-ray scattering (SAXS) images of breast tissue of three different pathologies: normal, benign and malignant. The objective was to thoroughly examine the images and detect those features indicative of malignancy. The tissue sample which is the source of the SAXS image is approximately ten millimetres long and one millimetre wide. In comparison, the structures of interest are on the nanometre scale and therefore we would expect that in practice each sample is a mixture of the different tissue pathologies. This mixture of different pathologies will have a bearing on the overall classification of the sample. Conventional classification models will tend to use data that has been reduced to those components that show the most variation. However in this case, even trivial amounts of feature suggestive of malignancy must be retained as they might be influential in the classification of tissue type. The mathematical strategy adopted in this thesis relied on a series of transforms along with the resulting interpretation of their coefficients. An adaptive transform that used a range of filter functions was applied to the SAXS images. The coefficients from this transform that had an acceptable probability of misclassification were retained and the others rejected.