Investigation of the convergence properties of an iterative image restoration algorithm.

Persistent Link:
http://hdl.handle.net/10150/186848
Title:
Investigation of the convergence properties of an iterative image restoration algorithm.
Author:
Elfendahl, Michael Preston.
Issue Date:
1994
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Iterative algorithms for image restoration which include the use of prior knowledge of the solution in their design have proven useful in super resolution imaging. In this dissertation, a Bayesian estimation method is presented called the Poisson Maximum A Posteriori (MAP) image restoration algorithm. The Poisson MAP algorithm is shown to be slightly different in its design but similar in super resolution ability to the Poisson Maximum Likelihood (ML) algorithm. Numerical simulations demonstrate that the Poisson MAP algorithm in almost all cases achieves legitimate bandwidth extension and thus achieves super resolution. Practical criteria for indicating when the algorithm has numerically converged are reviewed. The advantages of these criteria are discussed. The theoretical convergence properties of the Poisson MAP algorithm are investigated. The iterative algorithm is viewed as a nonlinear vector mapping in the N-dimensional real Euclidean vector space, Rᴺ. The necessary and sufficient conditions for nonlinear iterative methods of this type to converge are discussed and are shown to be satisfied in certain cases. Although convergence in some cases can only be demonstrated experimentally, convergence can almost always be guaranteed with the right choice of starting vector in cases where super resolution is most needed.
Type:
text; Dissertation-Reproduction (electronic)
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Hunt, B.R.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleInvestigation of the convergence properties of an iterative image restoration algorithm.en_US
dc.creatorElfendahl, Michael Preston.en_US
dc.contributor.authorElfendahl, Michael Preston.en_US
dc.date.issued1994en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIterative algorithms for image restoration which include the use of prior knowledge of the solution in their design have proven useful in super resolution imaging. In this dissertation, a Bayesian estimation method is presented called the Poisson Maximum A Posteriori (MAP) image restoration algorithm. The Poisson MAP algorithm is shown to be slightly different in its design but similar in super resolution ability to the Poisson Maximum Likelihood (ML) algorithm. Numerical simulations demonstrate that the Poisson MAP algorithm in almost all cases achieves legitimate bandwidth extension and thus achieves super resolution. Practical criteria for indicating when the algorithm has numerically converged are reviewed. The advantages of these criteria are discussed. The theoretical convergence properties of the Poisson MAP algorithm are investigated. The iterative algorithm is viewed as a nonlinear vector mapping in the N-dimensional real Euclidean vector space, Rᴺ. The necessary and sufficient conditions for nonlinear iterative methods of this type to converge are discussed and are shown to be satisfied in certain cases. Although convergence in some cases can only be demonstrated experimentally, convergence can almost always be guaranteed with the right choice of starting vector in cases where super resolution is most needed.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairHunt, B.R.en_US
dc.contributor.committeememberGreenlee, W. M.en_US
dc.contributor.committeememberSecomb, T. W.en_US
dc.identifier.proquest9506980en_US
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