Geometric Multiscale Analysis and Applications to Neuroscience Imaging

This thesis is concerned with the development of quantitative methods for the analysis of neuronal images. Automated detection and segmentation of components of neurons in fluorescent images is a major goal in quantitative studies of neuronal networks, including applications of high-content-screenings where one needs to compute multiple morphological properties of neurons. Despite recent advances in image processing targeted to neurobiological applications, existing algorithms of soma detection and neurite tracing still have significant limitations which are more severe when processing fluorescence image stacks of neuronal cultures. To address such challenges, in this dissertation, we develop several novel methods and algorithms aimed at extracting quantitative information in fluorescent images of neuronal cultures or brain tissue, including methods for the automated detection of the soma and other subcellullar structures of interest, and algorithms for cell classification. Our methods rely on technique from harmonic analysis, especially wavelets and more advanced multiscale representation systems. Using these techniques, we are able to extract highly informative image characteristics with high geometric sensitivity and computational efficiency. As part of our work, we include a theoretical justification and an extensive numerical validation on microscopy imaging data provided by our collaborators in neuriscience. An extensive comparison with state-of-the-art existing methods demonstrate that our algorithms are highly competitive in terms of accuracy, reliability and computational efficiency.Mathematics, Department o