Dynamical Sampling
dc.creator | Tang, Sui | |
dc.date.accessioned | 2020-08-22T17:01:01Z | |
dc.date.available | 2016-05-31 | |
dc.date.issued | 2016-05-31 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-05302016-212758 | |
dc.identifier.uri | http://hdl.handle.net/1803/12430 | |
dc.description.abstract | Let f ∈ l^2(I) be a signal at time t = 0 of an evolution process controlled by a bounded linear operator A that produces the signals A f , A^2 f , · · · at times t = 1, 2, · · · . Let Y = { f (i), Af (i), · · · , A^(l_i )f (i) : i ∈ Ω ⊂ I} be the spatio-temporal samples taken at various time levels. The problem under consideration is to find necessary and sufficient conditions on A, Ω, l_i in order to recover any f ∈ l^2(I) from the measurements Y . This is the so called Dynamical Sampling Problem in which we seek to recover a signal f by combining coarse samples of f and its futures states A^lf . Various versions of dynamical sampling problems exhibit features that are similar to many fundamental problems: deconvolution, filter banks, super-resolution, compressed sensing etc. In this dissertation, we will study these problems. | |
dc.format.mimetype | application/pdf | |
dc.subject | Sampling theory | |
dc.subject | Frame theory | |
dc.subject | channel estimation | |
dc.title | Dynamical Sampling | |
dc.type | dissertation | |
dc.contributor.committeeMember | Ed Saff | |
dc.contributor.committeeMember | Alex Powell | |
dc.contributor.committeeMember | Doug Hardin | |
dc.contributor.committeeMember | Akos Ledeczi | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2016-05-31 | |
local.embargo.lift | 2016-05-31 | |
dc.contributor.committeeChair | Akram Aldroubi |
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