Compressed Sensing Beyond the IID and Static Domains: Theory, Algorithms and Applications

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dc.contributor.advisorWu, Minen_US
dc.contributor.advisorBabadi, Behtashen_US
dc.contributor.authorKazemipour, Abbasen_US
dc.contributor.departmentElectrical Engineeringen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2018-01-25T06:31:24Z
dc.date.available2018-01-25T06:31:24Z
dc.date.issued2017en_US
dc.description.abstractSparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions using few measurements, where i.i.d measurements are at disposal. However real world scenarios typically exhibit non i.i.d and dynamic structures and are confined by physical constraints, preventing applicability of the theoretical guarantees of compressed sensing and limiting its applications. In this thesis we develop new theory, algorithms and applications for non i.i.d and dynamic compressed sensing by considering such constraints. In the first part of this thesis we derive new optimal sampling-complexity tradeoffs for two commonly used processes used to model dependent temporal structures: the autoregressive processes and self-exciting generalized linear models. Our theoretical results successfully recovered the temporal dependencies in neural activities, financial data and traffic data. Next, we develop a new framework for studying temporal dynamics by introducing compressible state-space models, which simultaneously utilize spatial and temporal sparsity. We develop a fast algorithm for optimal inference on such models and prove its optimal recovery guarantees. Our algorithm shows significant improvement in detecting sparse events in biological applications such as spindle detection and calcium deconvolution. Finally, we develop a sparse Poisson image reconstruction technique and the first compressive two-photon microscope which uses lines of excitation across the sample at multiple angles. We recovered diffraction-limited images from relatively few incoherently multiplexed measurements, at a rate of 1.5 billion voxels per second.en_US
dc.identifierhttps://doi.org/10.13016/M28S4JQ9Z
dc.identifier.urihttp://hdl.handle.net/1903/20407
dc.language.isoenen_US
dc.subject.pqcontrolledElectrical engineeringen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledStatisticsen_US
dc.subject.pquncontrolledcompressed sensingen_US
dc.subject.pquncontrolledcomputational neuroscienceen_US
dc.subject.pquncontrolledimage processingen_US
dc.subject.pquncontrolledneural signal processingen_US
dc.subject.pquncontrolledoptimizationen_US
dc.subject.pquncontrolledtwo-photon microscopyen_US
dc.titleCompressed Sensing Beyond the IID and Static Domains: Theory, Algorithms and Applicationsen_US
dc.typeDissertationen_US

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