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Mathematical topics in imaging: Sam...

Khare, Kedar.

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Mathematical topics in imaging: Sampling theory and eigenfunction analysis of imaging systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical topics in imaging: Sampling theory and eigenfunction analysis of imaging systems./
Author:	Khare, Kedar.
Description:	223 p.
Notes:	Source: Dissertation Abstracts International, Volume: 65-02, Section: B, page: 0816.
Contained By:	Dissertation Abstracts International65-02B.
Subject:	Physics, Optics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3122241
ISBN:	0496695916

Mathematical topics in imaging: Sampling theory and eigenfunction analysis of imaging systems.
Khare, Kedar.

Mathematical topics in imaging: Sampling theory and eigenfunction analysis of imaging systems. - 223 p.

Source: Dissertation Abstracts International, Volume: 65-02, Section: B, page: 0816.

Thesis (Ph.D.)--University of Rochester, 2004.

We use the Whittaker-Shannon sampling theorem as a guideline to explore several mathematical ideas that originate from problems in imaging. First a modified form of sampling theorem is derived for efficient sampling of carrier-frequency type signals and applied to direct coarse sampling and demodulation of electronic holograms. The concepts such as space-bandwidth product and uncertainty are studied in detail from the point of view of energy concentration and a connection between the sampling theorem and the eigenfunctions of the sinc-kernel (prolate spheroidal wave functions) is established. The prolate spheroids are further used to introduce a fractional version of the finite Fourier transform and the associated inverse problems are studied. The sampling formulae for carrier-frequency signals are employed to construct a new set of orthogonal functions---that we name as "bandpass prolate spheroids"---which is an efficient basis set for representing carrier-frequency type signals on finite intervals. The sampling theorem based treatment of prolate spheroids is then extended to study the eigenvalue problems associated with general bandlimited integral kernels and a non-iterative method for computing eigenwavefronts of linear space-invariant imaging systems (including aberrated ones) is presented. An important result established in this analysis is that the number of significant eigenvalues of an imaging system is of the order of its space-bandwidth product. A definition for the space-bandwidth product or the information carrying capacity of an imaging system is proposed with the help of eigenwavefronts. The application of eigenwavefronts to inverse or de-convolution problems in imaging is also demonstrated.

ISBN: 0496695916Subjects--Topical Terms:

1018756
Physics, Optics.

Mathematical topics in imaging: Sampling theory and eigenfunction analysis of imaging systems.
LDR:02644nmm 2200277 4500 001 1848190
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020 $a 0496695916
035 $a (UnM)AAI3122241
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040 $a UnM $c UnM
100 1 $a Khare, Kedar. $3 1936207
245 1 0 $a Mathematical topics in imaging: Sampling theory and eigenfunction analysis of imaging systems.
300 $a 223 p.
500 $a Source: Dissertation Abstracts International, Volume: 65-02, Section: B, page: 0816.
500 $a Supervisor: Nicholas George.
502 $a Thesis (Ph.D.)--University of Rochester, 2004.
520 $a We use the Whittaker-Shannon sampling theorem as a guideline to explore several mathematical ideas that originate from problems in imaging. First a modified form of sampling theorem is derived for efficient sampling of carrier-frequency type signals and applied to direct coarse sampling and demodulation of electronic holograms. The concepts such as space-bandwidth product and uncertainty are studied in detail from the point of view of energy concentration and a connection between the sampling theorem and the eigenfunctions of the sinc-kernel (prolate spheroidal wave functions) is established. The prolate spheroids are further used to introduce a fractional version of the finite Fourier transform and the associated inverse problems are studied. The sampling formulae for carrier-frequency signals are employed to construct a new set of orthogonal functions---that we name as "bandpass prolate spheroids"---which is an efficient basis set for representing carrier-frequency type signals on finite intervals. The sampling theorem based treatment of prolate spheroids is then extended to study the eigenvalue problems associated with general bandlimited integral kernels and a non-iterative method for computing eigenwavefronts of linear space-invariant imaging systems (including aberrated ones) is presented. An important result established in this analysis is that the number of significant eigenvalues of an imaging system is of the order of its space-bandwidth product. A definition for the space-bandwidth product or the information carrying capacity of an imaging system is proposed with the help of eigenwavefronts. The application of eigenwavefronts to inverse or de-convolution problems in imaging is also demonstrated.
590 $a School code: 0188.
650 4 $a Physics, Optics. $3 1018756
650 4 $a Engineering, Electronics and Electrical. $3 626636
690 $a 0752
690 $a 0544
710 2 0 $a University of Rochester. $3 515736
773 0 $t Dissertation Abstracts International $g 65-02B.
790 1 0 $a George, Nicholas, $e advisor
790 $a 0188
791 $a Ph.D.
792 $a 2004
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3122241