Projection based image restoration, super-resolution and error correction codes

Persistent Link:
http://hdl.handle.net/10150/284043
Title:
Projection based image restoration, super-resolution and error correction codes
Author:
Bauer, Karl Gregory
Issue Date:
1999
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:
Super-resolution is the ability of a restoration algorithm to restore meaningful spatial frequency content beyond the diffraction limit of the imaging system. The Gerchberg-Papoulis (GP) algorithm is one of the most celebrated algorithms for super-resolution. The GP algorithm is conceptually simple and demonstrates the importance of using a priori information in the formation of the object estimate. In the first part of this dissertation the continuous GP algorithm is discussed in detail and shown to be a projection on convex sets algorithm. The discrete GP algorithm is shown to converge in the exactly-, over- and under-determined cases. A direct formula for the computation of the estimate at the kth iteration and at convergence is given. This analysis of the discrete GP algorithm sets the stage to connect super-resolution to error-correction codes. Reed-Solomon codes are used for error-correction in magnetic recording devices, compact disk players and by NASA for space communications. Reed-Solomon codes have a very simple description when analyzed with the Fourier transform. This signal processing approach to error-correction codes allows the error-correction problem to be compared with the super-resolution problem. The GP algorithm for super-resolution is shown to be equivalent to the correction of errors with a Reed-Solomon code over an erasure channel. The Restoration from Magnitude (RFM) problem seeks to recover a signal from the magnitude of the spectrum. This problem has applications to imaging through a turbulent atmosphere. The turbulent atmosphere causes localized changes in the index of refraction and introduces different phase delays in the data collected. Synthetic aperture radar (SAR) and hyperspectral imaging systems are capable of simultaneously recording multiple images of different polarizations or wavelengths. Each of these images will experience the same turbulent atmosphere and have a common phase distortion. A projection based restoration algorithm for the simultaneous restoration of pairs of images experiencing a common phase distortion is presented.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Applied Mechanics.; Engineering, Electronics and Electrical.; Physics, Optics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Marcellin, Michael W.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleProjection based image restoration, super-resolution and error correction codesen_US
dc.creatorBauer, Karl Gregoryen_US
dc.contributor.authorBauer, Karl Gregoryen_US
dc.date.issued1999en_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.abstractSuper-resolution is the ability of a restoration algorithm to restore meaningful spatial frequency content beyond the diffraction limit of the imaging system. The Gerchberg-Papoulis (GP) algorithm is one of the most celebrated algorithms for super-resolution. The GP algorithm is conceptually simple and demonstrates the importance of using a priori information in the formation of the object estimate. In the first part of this dissertation the continuous GP algorithm is discussed in detail and shown to be a projection on convex sets algorithm. The discrete GP algorithm is shown to converge in the exactly-, over- and under-determined cases. A direct formula for the computation of the estimate at the kth iteration and at convergence is given. This analysis of the discrete GP algorithm sets the stage to connect super-resolution to error-correction codes. Reed-Solomon codes are used for error-correction in magnetic recording devices, compact disk players and by NASA for space communications. Reed-Solomon codes have a very simple description when analyzed with the Fourier transform. This signal processing approach to error-correction codes allows the error-correction problem to be compared with the super-resolution problem. The GP algorithm for super-resolution is shown to be equivalent to the correction of errors with a Reed-Solomon code over an erasure channel. The Restoration from Magnitude (RFM) problem seeks to recover a signal from the magnitude of the spectrum. This problem has applications to imaging through a turbulent atmosphere. The turbulent atmosphere causes localized changes in the index of refraction and introduces different phase delays in the data collected. Synthetic aperture radar (SAR) and hyperspectral imaging systems are capable of simultaneously recording multiple images of different polarizations or wavelengths. Each of these images will experience the same turbulent atmosphere and have a common phase distortion. A projection based restoration algorithm for the simultaneous restoration of pairs of images experiencing a common phase distortion is presented.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectApplied Mechanics.en_US
dc.subjectEngineering, Electronics and Electrical.en_US
dc.subjectPhysics, Optics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorMarcellin, Michael W.en_US
dc.identifier.proquest9960238en_US
dc.identifier.bibrecord.b40271833en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.