Date of Award

Spring 5-10-2020

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

David Bradley

Second Committee Member

Andre Khalil

Third Committee Member

Peter Stechlinski

Abstract

The CompuMAINE lab has developed a patented computational cancer detection method utilizing the 2D Wavelet Transform Modulus Maxima (WTMM) method to help predict disrupted, tumor-associated breast tissue from mammography. The lab has a database of mammograms in which some of the image subregions contain artefacts which are excluded from the analysis, image saturation is one such artefact. To maximize statistical power in our clinical analyses, our goal is therefore to minimize the rejection of image subregions containing artefacts. The goal of this particular project is to explore the effects of image saturation on the resulting multifractal statistics from the 2D WTMM method. Groups of numerically simulated (monofractal) fractional Brownian motion (fBm) surfaces with varying roughness exponents were generated and saturated at the 1\%, 5\%, 10\% and 20\% levels. We find that image saturation reduces the range of available statistical order moments relative to an unsaturated image. By assessing the effects of image saturation on the 2D WTMM calculations, we developed a filtering approach where we nearly regained the entire range of statistical order moments thus limiting the impacts of image saturation.

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