Alternating minimization multigrid algorithms for transmission tomography

Joseph A. O'Sullivan; Jasenka Benac

doi:10.1117/12.537508

Alternating minimization multigrid algorithms for transmission tomography

Joseph A. O'Sullivan
, Jasenka Benac

Research output: Contribution to journal › Conference article › peer-review

4 Scopus citations

Abstract

The problem of image formation for X-ray transmission tomography is formulated as a statistical inverse problem. The maximum likelihood estimate of the attenuation function is sought. Using convex optimization methods, maximizing the log-likelihood functional is equivalent to a double minimization of I-divergence, one of the minimizations being over the attenuation function. Restricting the minimization over the attenuation function to a coarse grid component forms the basis for a multigrid algorithm that is guaranteed to monotonically decrease the I-divergence at every iteration on every scale.

Original language	English
Pages (from-to)	216-221
Number of pages	6
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	5299
DOIs	https://doi.org/10.1117/12.537508
State	Published - 2004
Event	Computational Imaging II - San Jose, CA, United States Duration: Jan 19 2004 → Jan 20 2004

Keywords

Alternating minimization algorithms
CT imaging
Expectation maximization algorithm
Multigrid methods
Transmission tomography

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10.1117/12.537508

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abstract = "The problem of image formation for X-ray transmission tomography is formulated as a statistical inverse problem. The maximum likelihood estimate of the attenuation function is sought. Using convex optimization methods, maximizing the log-likelihood functional is equivalent to a double minimization of I-divergence, one of the minimizations being over the attenuation function. Restricting the minimization over the attenuation function to a coarse grid component forms the basis for a multigrid algorithm that is guaranteed to monotonically decrease the I-divergence at every iteration on every scale.",

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AU - Benac, Jasenka

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N2 - The problem of image formation for X-ray transmission tomography is formulated as a statistical inverse problem. The maximum likelihood estimate of the attenuation function is sought. Using convex optimization methods, maximizing the log-likelihood functional is equivalent to a double minimization of I-divergence, one of the minimizations being over the attenuation function. Restricting the minimization over the attenuation function to a coarse grid component forms the basis for a multigrid algorithm that is guaranteed to monotonically decrease the I-divergence at every iteration on every scale.

AB - The problem of image formation for X-ray transmission tomography is formulated as a statistical inverse problem. The maximum likelihood estimate of the attenuation function is sought. Using convex optimization methods, maximizing the log-likelihood functional is equivalent to a double minimization of I-divergence, one of the minimizations being over the attenuation function. Restricting the minimization over the attenuation function to a coarse grid component forms the basis for a multigrid algorithm that is guaranteed to monotonically decrease the I-divergence at every iteration on every scale.

KW - Alternating minimization algorithms

KW - CT imaging

KW - Expectation maximization algorithm

KW - Multigrid methods

KW - Transmission tomography

UR - https://www.scopus.com/pages/publications/8844274053

U2 - 10.1117/12.537508

DO - 10.1117/12.537508

M3 - Conference article

AN - SCOPUS:8844274053

SN - 0277-786X

VL - 5299

SP - 216

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JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

T2 - Computational Imaging II

Y2 - 19 January 2004 through 20 January 2004

ER -

Alternating minimization multigrid algorithms for transmission tomography

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