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Sparse Signal Representation in Digital and Biological Systems

dc.contributor.advisorCzaja, Wojciechen_US
dc.contributor.authorGuay, Matthewen_US
dc.description.abstractTheories of sparse signal representation, wherein a signal is decomposed as the sum of a small number of constituent elements, play increasing roles in both mathematical signal processing and neuroscience. This happens despite the differences between signal models in the two domains. After reviewing preliminary material on sparse signal models, I use work on compressed sensing for the electron tomography of biological structures as a target for exploring the efficacy of sparse signal reconstruction in a challenging application domain. My research in this area addresses a topic of keen interest to the biological microscopy community, and has resulted in the development of tomographic reconstruction software which is competitive with the state of the art in its field. Moving from the linear signal domain into the nonlinear dynamics of neural encoding, I explain the sparse coding hypothesis in neuroscience and its relationship with olfaction in locusts. I implement a numerical ODE model of the activity of neural populations responsible for sparse odor coding in locusts as part of a project involving offset spiking in the Kenyon cells. I also explain the validation procedures we have devised to help assess the model's similarity to the biology. The thesis concludes with the development of a new, simplified model of locust olfactory network activity, which seeks with some success to explain statistical properties of the sparse coding processes carried out in the network.en_US
dc.titleSparse Signal Representation in Digital and Biological Systemsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.subject.pqcontrolledApplied mathematicsen_US
dc.subject.pqcontrolledArtificial intelligenceen_US
dc.subject.pquncontrolledbiomedical imagingen_US
dc.subject.pquncontrolledcompressed sensingen_US
dc.subject.pquncontrolledelectron tomographyen_US
dc.subject.pquncontrolledsparse neural codingen_US

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