Computer aided diagnostic tool can aid the radiologist in the early detection of breast cancer. Even though mammography is considered to be the gold standard for breast cancer detection, it is limited by the spatial superposition of tissue. This limitation is the result of a using a two dimensional, (2D), representation of a three dimensional, (3D), structure. The limitation contributes to and results in misclassification of breast cancers. Tomosynthesis is a limited-angle 3D imaging device that overcomes this limitation by representing the breast structure with 3D volumetric data.This research, on tomosynthesis imaging, was a critical module of a larger research endeavor for the detection of breast cancer. Tomosynthesis is an emerging state-of-the-art 3D imaging technology. The purpose of this research was to develop a tomosynthesis based, efficient suspicious region segmentation, procedure for the breast to enhance the detection and diagnosis of breast cancer. The 3D breast volume is constructed to visualize the 3D structure of the breast region. Advanced image processing and analysis algorithms were developed to remove out-of-plane artifacts and increase the Signal Difference to Noise Ratio, (SDNR), of tomosynthetic images. Suspicious regions are extracted from the breast volume using efficient and robust clustering algorithms.A partial differential equation based non-linear diffusion method was modified to include the anisotropic nature of tomosynthesis data in order to filter out the out-of-plane artifacts, which are termed "tomosynthetic noise", and to smooth the in-plane noise. Fuzzy clustering algorithms were modified to include spatial domain information to segment suspicious regions. A significant improvement was observed, both qualitatively and quantitatively, in segmentation of the filtered data over the non-filtered data. The 3D segmentation system is robust enough to be used for statistical analysis of huge databases.

In this thesis we study Sobolev gradient flows for Perona-Malik style energy functionals and generalizations thereof. We begin with first order isotropic flows which are shown to be regularizations of the heat equation. We show that these flows are well-posed in the forward and reverse directions which yields an effective linear sharpening algorithm. We furthermore establish a number of maximum principles for the forward flow and show that edges are preserved for a finite period of time. We then go on to study isotropic Sobolev gradient flows with respect to higher order Sobolev metrics. As the Sobolev order is increased, we observe an increasing reluctance to destroy fine details and texture. We then consider Sobolev gradient flows for non-linear anisotropic diffusion functionals of arbitrary order. We establish existence, uniqueness and continuous dependence on initial data for a broad class of such equations. The well-posedness of these new anisotropic gradient flows opens the door to a wide variety of sharpening and diffusion techniques which were previously impossible under L2 gradient descent. We show how one can easily use this framework to design an anisotropic sharpening algorithm which can sharpen image features while suppressing noise. We compare our sharpening algorithm to the well-known shock filter and show that Sobolev sharpening produces natural looking images without the "staircasing" artifacts that plague the shock filter. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2010-08-25 10:44:12.23

The master thesis is focused on the principle of ultrasonographs and their modes, and ways of denoising data obtained by ultrasonographs. This project will also concentrate on removing the speckle noise, because the speckle noise has the largest share of the noise in the measured data in ultrasonographs. The other main objective was to describe advanced methods of filtration, especially the modifications of the median filter, such as the modified hybrid median filter and modification of the anisotropic diffusion, namely generalizing Perona-Malik anisotropic diffusion using restricted dissimilarity functions. These two filters were tested on images with artificial noise and on data captured using the ultrasound system GE VingMed System FiVe. Also, the program for filtering and display filtered ultrasound data captured by GE VingMed System FiVe is described.