Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography

Wenwu Zhu, Yao Wang, Yining Deng, Yuqi Yao, Randall L. Barbour

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we present a wavelet based multigrid approach to solve the perturbation equation encountered in optical tomography. With this scheme, the unknown image, the data, as well as weight matrix are all represented by wavelet expansions, and thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level, a regularized least squares solution is obtained using a conjugate gradient descent method. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsRandall L. Barbour, Mark J. Carvlin, Michael A. Fiddy
Pages186-196
Number of pages11
Volume2570
StatePublished - 1995
EventExperimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications - San Diego, CA, USA
Duration: Jul 10 1995Jul 11 1995

Other

OtherExperimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications
CitySan Diego, CA, USA
Period7/10/957/11/95

Fingerprint

Optical tomography
image reconstruction
Image reconstruction
tomography
multigrid methods
perturbation
descent
grids
gradients
expansion
coefficients
matrices
approximation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Zhu, W., Wang, Y., Deng, Y., Yao, Y., & Barbour, R. L. (1995). Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography. In R. L. Barbour, M. J. Carvlin, & M. A. Fiddy (Eds.), Proceedings of SPIE - The International Society for Optical Engineering (Vol. 2570, pp. 186-196)

Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography. / Zhu, Wenwu; Wang, Yao; Deng, Yining; Yao, Yuqi; Barbour, Randall L.

Proceedings of SPIE - The International Society for Optical Engineering. ed. / Randall L. Barbour; Mark J. Carvlin; Michael A. Fiddy. Vol. 2570 1995. p. 186-196.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Zhu, W, Wang, Y, Deng, Y, Yao, Y & Barbour, RL 1995, Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography. in RL Barbour, MJ Carvlin & MA Fiddy (eds), Proceedings of SPIE - The International Society for Optical Engineering. vol. 2570, pp. 186-196, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, San Diego, CA, USA, 7/10/95.
Zhu W, Wang Y, Deng Y, Yao Y, Barbour RL. Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography. In Barbour RL, Carvlin MJ, Fiddy MA, editors, Proceedings of SPIE - The International Society for Optical Engineering. Vol. 2570. 1995. p. 186-196
Zhu, Wenwu ; Wang, Yao ; Deng, Yining ; Yao, Yuqi ; Barbour, Randall L. / Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography. Proceedings of SPIE - The International Society for Optical Engineering. editor / Randall L. Barbour ; Mark J. Carvlin ; Michael A. Fiddy. Vol. 2570 1995. pp. 186-196
@inproceedings{855d06dd67ae4ec888011e5b1972f949,
title = "Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography",
abstract = "In this paper, we present a wavelet based multigrid approach to solve the perturbation equation encountered in optical tomography. With this scheme, the unknown image, the data, as well as weight matrix are all represented by wavelet expansions, and thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level, a regularized least squares solution is obtained using a conjugate gradient descent method. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.",
author = "Wenwu Zhu and Yao Wang and Yining Deng and Yuqi Yao and Barbour, {Randall L.}",
year = "1995",
language = "English (US)",
isbn = "081941929X",
volume = "2570",
pages = "186--196",
editor = "Barbour, {Randall L.} and Carvlin, {Mark J.} and Fiddy, {Michael A.}",
booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",

}

TY - GEN

T1 - Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography

AU - Zhu, Wenwu

AU - Wang, Yao

AU - Deng, Yining

AU - Yao, Yuqi

AU - Barbour, Randall L.

PY - 1995

Y1 - 1995

N2 - In this paper, we present a wavelet based multigrid approach to solve the perturbation equation encountered in optical tomography. With this scheme, the unknown image, the data, as well as weight matrix are all represented by wavelet expansions, and thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level, a regularized least squares solution is obtained using a conjugate gradient descent method. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.

AB - In this paper, we present a wavelet based multigrid approach to solve the perturbation equation encountered in optical tomography. With this scheme, the unknown image, the data, as well as weight matrix are all represented by wavelet expansions, and thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level, a regularized least squares solution is obtained using a conjugate gradient descent method. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.

UR - http://www.scopus.com/inward/record.url?scp=0029482864&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029482864&partnerID=8YFLogxK

M3 - Conference contribution

SN - 081941929X

SN - 9780819419293

VL - 2570

SP - 186

EP - 196

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

A2 - Barbour, Randall L.

A2 - Carvlin, Mark J.

A2 - Fiddy, Michael A.

ER -