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dc.contributor.advisor Zhang, Yin
dc.creatorCastanon, Jorge Castanon Alberto
dc.date.accessioned 2016-01-06T20:52:57Z
dc.date.available 2016-01-06T20:52:57Z
dc.date.created 2015-05
dc.date.issued 2015-04-20
dc.date.submitted May 2015
dc.identifier.citation Castanon, Jorge Castanon Alberto. "A Spectrum-based Regularization Approach to Linear Inverse Problems: Models, Learned Parameters and Algorithms." (2015) Diss., Rice University. https://hdl.handle.net/1911/87728.
dc.identifier.urihttps://hdl.handle.net/1911/87728
dc.description.abstract In this thesis, we study the problem of recovering signals, in particular images, that approximately satisfy severely ill-conditioned or underdetermined linear systems. For example, such a linear system may represent a set of under-sampled and noisy linear measurements. It is well-known that the quality of the recovery critically depends on the choice of an appropriate regularization model that incorporates prior information about the target solution. Two of the most successful regularization models are the Tikhonov and Total Variation (TV) models, each of which is used in a wide range of applications. We design and investigate a class of spectrum-based models that generalize and improve upon both the Tikhonov and the TV methods, as well as their combinations or so-called hybrids. The proposed models contain "spectrum parameters" that are learned from training data sets through solving optimization problems. This parameter-learning feature gives these models the flexibility to adapt to desired target solutions. We devise efficient algorithms for all the proposed models and conduct comprehensive numerical experiments to evaluate their performance as compared to established models. Numerical results show a generally superior quality in recovered images by our approach from under-sampled linear measurements. Using the proposed algorithms, one can often obtain much improved quality at a moderate increase in computational time.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectnumerical optimization
regularization
linear inverse problems: machine learning
image recovery
compressive sensing
dc.title A Spectrum-based Regularization Approach to Linear Inverse Problems: Models, Learned Parameters and Algorithms
dc.contributor.committeeMember Tapia, Richard
dc.contributor.committeeMember Hand, Paul
dc.contributor.committeeMember Kelly, Kevin
dc.date.updated 2016-01-06T20:52:57Z
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Computational and Applied Mathematics
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy


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