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Title page for ETD etd-06152017-210945

Type of Document Dissertation
Author Lee, Chang Hsin
Author's Email Address lee.changhsin@gmail.com
URN etd-06152017-210945
Title Analysis of Signal Reconstruction Algorithms Based on Consistency Constraints
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Alexander Powell Committee Chair
Akram Aldroubi Committee Member
Brett Byram Committee Member
Doug Hardin Committee Member
Mike Neamtu Committee Member
  • digital signal processing
  • consistent reconstruction
  • Rangan-Goyal algorithm
  • signal reconstruction
Date of Defense 2017-04-17
Availability unrestricted
A fundamental problem in signal processing called signal reconstruction, or signal recovery, is the determination of a signal from a sequence of samples obtained

from the signal. The sampling process can be viewed as obtaining measurements from

a set of measurement vectors in an N-dimensional space. Studies on the reconstruction problem have resulted

in major breakthroughs in technology in the past century, and practical solutions to the

problem are still essential in the advancement of fields such as image processing and speech


Consistent reconstruction and Rangan-Goyal algorithm are two algorithms that produce

estimates of a signal from consistency constraints when the measurements are

corrupted with i.i.d uniformly distributed noises. Under the assumption that the

measurements are taken with i.i.d. unit-norm random vectors, the second error moments

of both algorithms are known to converge with a rate of O(N^2). In this work, we showed

that the general p-th error moments of both algorithms converge with a rate of O(N^p)

under general admissibility conditions on the sampling distribution that no longer require

the measurement vectors to be unit-norm.

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