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Dynamical Sampling and its Applications

dc.creatorHuang, Longxiu
dc.date.accessioned2020-08-21T21:16:11Z
dc.date.available2019-03-22
dc.date.issued2019-03-22
dc.identifier.urietd-03192019-114134
dc.identifier.urihttp://hdl.handle.net/1803/10916
dc.description.abstractDynamical sampling is a new area in sampling theory that deals with signals that evolve over time under the action of a linear operator. There are lots of studies on various aspects of the dynamical sampling problem. However, they all focus on uniform discrete time-sets $mathcal{T} subset mathbb{N}$. In our first paper, we concentrate on the case $mathcal{T} = [0, L]$. The goal of the present work is to study the frame property of the systems ${A^tg : g inmathcal{G}, t in [0, L]}$. To this end, we also characterize the completeness and Besselness properties of these systems. In our second paper, we consider dynamical sampling when the samples are corrupted by additive noises. The purpose of the second paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and study the impact of additive noise. The algorithms are implemented and tested on synthetic and real data sets, and denoising techniques are integrated to mitigate the effect of the noise. We also develop theoretical and numerical results that validate the algorithm for recovering the driving operators, which are defined via a real symmetric convolution.
dc.format.mimetypeapplication/pdf
dc.subjectCadzow denoising algorithm
dc.subjectnumerical linear algebra
dc.subjectcontinuous frames
dc.subjectdynamical sampling
dc.titleDynamical Sampling and its Applications
dc.typedissertation
dc.contributor.committeeMemberAlexander M. Powell
dc.contributor.committeeMemberLarry L. Schumaker
dc.contributor.committeeMemberDavid S. Smith
dc.contributor.committeeMemberDouglas P. Hardin
dc.type.materialtext
thesis.degree.namePHD
thesis.degree.leveldissertation
thesis.degree.disciplineMathematics
thesis.degree.grantorVanderbilt University
local.embargo.terms2019-03-22
local.embargo.lift2019-03-22
dc.contributor.committeeChairAkram Aldroubi


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