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Title page for ETD etd-05302016-212758


Type of Document Dissertation
Author Tang, Sui
Author's Email Address rosier1989@gmail.com
URN etd-05302016-212758
Title Dynamical Sampling
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Akram Aldroubi Committee Chair
Akos Ledeczi Committee Member
Alex Powell Committee Member
Doug Hardin Committee Member
Ed Saff Committee Member
Keywords
  • Sampling theory
  • Frame theory
  • channel estimation
Date of Defense 2016-04-20
Availability unrestricted
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.

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