Let $f in ell^2(I)$ be a signal at time $t = 0$ of an evolution process controlled by a bounded linear operator A that produces the signals $Af, A^2f, cdots $ at times $t=1,2,cdots$. Let $Y ={f(i), Af(i), cdots, A^{l_i}f(i) : i in Omega subset I}$ be the spatio-temporal samples taken at various time levels. The problem under consideration is to find necessary and sufficient conditions on $A, Omega, l_i$ in order to recover any $f in ell^2(I)$ 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.
| Identifer | oai:union.ndltd.org:VANDERBILT/oai:VANDERBILTETD:etd-05302016-212758 |
| Date | 31 May 2016 |
| Creators | Tang, Sui |
| Contributors | Ed Saff, Alex Powell, Akram Aldroubi, Doug Hardin, Akos Ledeczi |
| Publisher | VANDERBILT |
| Source Sets | Vanderbilt University Theses |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.vanderbilt.edu/available/etd-05302016-212758/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Vanderbilt University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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