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dc.contributor.advisorMcClellan, James
dc.contributor.authorTurnes, Christopher Kowalczyk
dc.date.accessioned2014-05-22T15:32:02Z
dc.date.available2014-05-22T15:32:02Z
dc.date.created2014-05
dc.date.issued2014-04-04
dc.date.submittedMay 2014
dc.identifier.urihttp://hdl.handle.net/1853/51878
dc.description.abstractThis research develops efficient solution methods for linear systems with scalar and multi-level Toeplitz structure. Toeplitz systems are common in one-dimensional signal-processing applications, and typically correspond to temporal- or spatial-invariance in the underlying physical phenomenon. Over time, a number of algorithms have been developed to solve these systems economically by exploiting their structure. These developments began with the Levinson-Durbin recursion, a classical fast method for solving Toeplitz systems that has become a standard algorithm in signal processing. Over time, more advanced routines known as superfast algorithms were introduced that are capable of solving Toeplitz systems with even lower asymptotic complexity. For multi-dimensional signals, temporally- and spatially-invariant systems have linear-algebraic descriptions characterized by multi-level Toeplitz matrices, which exhibit Toeplitz structure on multiple levels. These matrices lack the same algebraic properties and structural simplicity of their scalar analogs. As a result, it has proven exceedingly difficult to extend the existing scalar Toeplitz algorithms for their treatment. This research presents algorithms to solve scalar and two-level Toeplitz systems through a constructive approach, using methods devised for specialized cases to build more general solution methods. These methods extend known scalar Toeplitz inversion results to more general scalar least-squares problems and to multi-level Toeplitz problems. The resulting algorithms have the potential to provide substantial computational gains for a large class of problems in signal processing, such as image deconvolution, non-uniform resampling, and the reconstruction of spatial volumes from non-uniform Fourier samples.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectMulti-level toeplitz
dc.subjectSuperfast algorithms
dc.subjectStructured linear algebra
dc.subjectToeplitz inversion
dc.subjectDigital resampling
dc.subjectNon-uniform FFTs
dc.subject3-D MRI
dc.subject.lcshSignal processing
dc.subject.lcshToeplitz matrices
dc.subject.lcshAlgorithms
dc.titleEfficient solutions to Toeplitz-structured linear systems for signal processing
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentElectrical and Computer Engineering
thesis.degree.levelDoctoral
dc.contributor.committeeMemberRomberg, Justin
dc.contributor.committeeMemberBarnes, Christopher
dc.contributor.committeeMemberHayes, Monson H.
dc.contributor.committeeMemberPoulson, Jack
dc.contributor.committeeMemberBalcan, Doru
dc.date.updated2014-05-22T15:32:02Z


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