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/ |
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