| Type of Document |
Dissertation |
| Author |
Leonetti, Casey Clark
|
| Author's Email Address |
casey.leonetti@alumni.vanderbilt.edu |
| URN |
etd-03292007-180005 |
| Title |
Reconstruction from Error-Affected Sampled Data in Shift-Invariant Spaces |
| Degree |
PhD |
| Department |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Akram Aldroubi |
Committee Chair |
| Benoit Dawant |
Committee Member |
| Douglas P. Hardin |
Committee Member |
| Guoliang Yu |
Committee Member |
| Larry Schumaker |
Committee Member |
|
| Keywords |
- jitter
- noise
- sampling
- shift-invariant space
- frame
- fourier
|
| Date of Defense |
2007-03-28 |
| Availability |
unrestricted |
Abstract
In the following chapters we provide error estimates for signals reconstructed from corrupt data. Two different types of error are considered. First, we address the problem of reconstructing a continuous function defined on Rd from a countable collection of samples corrupted by noise. The additive noise is assumed to be i.i.d. with mean 0 and variance σ2. We sample the continuous function f on the uniform lattice (1/m)Zd and show for large enough m that the variance of the error between the frame reconstruction fε from noisy samples of f and the function f satisfy var(fε (x)-f(x))≈ (σ2/md)Cx. Second, we address the problem of non-uniform sampling and reconstruction in the presence of jitter. In sampling applications, the set X={xj: j ∈ J} on which a signal f is sampled is not precisely known. Two main questions are considered. First, if sampling a function f on the countable set X leads to unique and stable reconstruction of f, then when does sampling on the set X'={xj+δj: j ∈ J} also lead to unique and stable reconstruction? Second, if we attempt to recover a sampled function f using the reconstruction operator corresponding to the sampling set X (because the precise sample points are unknown), is the recovered function a good approximation of the original f?
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| Filename |
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dissertation.pdf |
344.81 Kb |
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