Deep learning for neuroscience imaging and convolutional framelets using a tensor representation

My dissertation focuses on two problems: exploring image-based features for disease prediction and using techniques from tensor analysis to expand convolutional framelets to multivariate signals. The first problem is motivated by the outstanding need to better understand the molecular mechanisms underlying progress and onset of complex neuropsychiatric disorders such as schizophrenia. Previous research using human induced pluripotent stem cells has suggested alterations in a kinase signaling pathway associated with the neuronal cytoskeleton as a disease related feature in schizophrenia. We developed an approach integrating model based image analysis techniques, which are designed to capture changes in micro-structures, and data-driven learning techniques which can be used to predict the presence of the disease at the single-cell level. The second problem is motivated by the success of patch-based representations as an efficient signal representation for image analysis. Convolutional framelets are a novel univariate representation which integrates local and nonlocal properties of the signal. We investigate the extension to multivariate signals by adapting tensor techniques to derive a bivariate representation.