Image Analysis and Inferential Statistics with Medical Data
The goal of this project is to explore the latest mathematical approaches for image analysis and to create new results that will be tested on medical data such as high resolution retina scans from patients with some stage of diabetic retinopathy or CT scans from patients who were susceptible of developing lung cancer.
For image analysis we consider concepts developed in spectral graph theory along with variational methods from fluid dynamics and material science. The graph theoretic approach is motivated by the affinities between various locations in the images and we consider nonlocal total variation methods in order to address the diffusive interfaces or transitions between the different regions. The final goal is to improve the detection of patterns that are also clinically confirmed and indicative of the presence and the stage of the illness.