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dc.contributor.advisorWakin, Michael B.
dc.contributor.authorYang, Dehui
dc.date.accessioned2018-02-28T16:42:26Z
dc.date.accessioned2022-02-03T13:15:21Z
dc.date.available2018-02-28T16:42:26Z
dc.date.available2022-02-03T13:15:21Z
dc.date.issued2018
dc.identifierYang_mines_0052E_11442.pdf
dc.identifierT 8443
dc.identifier.urihttps://hdl.handle.net/11124/172154
dc.descriptionIncludes bibliographical references.
dc.description2018 Spring.
dc.description.abstractFrom single-molecule microscopy in biology, to collaborative filtering in recommendation systems, to quantum state tomography in physics, many scientific discoveries involve solving ill-posed inverse problems, where the number of parameters to be estimated far exceeds the number of available measurements. To make these daunting problems solvable, low-dimensional geometric structures are often exploited, and regularizations that promote underlying structures are used for various inference tasks. To date, one of the most effective and plausible low-dimensional models for matrix data is the low-rank structure, which assumes that columns of the data matrix are correlated and lie in a low-dimensional subspace. This helps make certain matrix inverse problems well-posed. However, in some cases, standard low-rank structure is not powerful enough for modeling the underlying data generating process, and additional modeling efforts are desired. This is the main focus of this research. Motivated by applications from different disciplines in engineering and science, in this dissertation, we consider the recovery of three instances of structured matrices from limited measurement data, where additional structures naturally occur in the data matrices beyond simple low-rankness. The structured matrices that we consider include i) low-rank and spectrally sparse matrices in super-resolution imaging; ii) low-rank skew-symmetric matrices in pairwise comparisons; iii) and low-rank positive semidefinite matrices in physical and data sciences. Using optimization as a tool, we develop new regularizers and computationally efficient algorithmic frameworks to account for structured low-rankness in solving these ill-posed inverse problems. For some of the problems considered in this dissertation, theoretical analysis is also carried out for the proposed optimization programs. We show that, under mild conditions, the structured low-rank matrices can be recovered reliably from a minimal number of random measurements.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado School of Mines. Arthur Lakes Library
dc.relation.ispartof2010-2019 - Mines Theses & Dissertations
dc.rightsCopyright of the original work is retained by the author.
dc.subjectmatrix completion
dc.subjectmodels
dc.subjectsuper-resolution
dc.subjectmodal analysis
dc.subjectlow-rank
dc.subjectoptimization
dc.titleStructured low-rank matrix recovery via optimization methods
dc.typeText
dc.contributor.committeememberVincent, Tyrone
dc.contributor.committeememberYang, Dejun
dc.contributor.committeememberTang, Gongguo
thesis.degree.nameDoctor of Philosophy (Ph.D.)
thesis.degree.levelDoctoral
thesis.degree.disciplineElectrical Engineering
thesis.degree.grantorColorado School of Mines


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