Abstract

In this paper, a spatial location weighted gradient-based optimization scheme for reducing the computation burden and increasing the reconstruction precision is stated. The method applies to DC diffusion-based optical tomography, where otherwise the reconstruction suffers slow convergence. The inverse approach employs a weighted steepest descent method combined with a conjugate gradient method. A reverse differentiation method is used to efficiently derive the gradient. The reconstruction results confirm that the spatial location weighted optimization method offers a more efficient approach to the DC optical imaging problem than unweighted method does.

© 2002 Optical Society of America

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References

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Advances in Engineering Software

A. J. Davies, D. B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, �??Reverse differentiation and the inverse diffusion problem,�?? Advances in Engineering Software 28, 217-221 (1997)
[CrossRef]

Appl. Opt.

S. R. Arridge, M. Schweiger, �??Photon-measurement density functions. Part2: Finite-element-method calculations,�?? Appl. Opt. 34, 8026-8037 (1995)
[CrossRef] [PubMed]

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S. S. Barbour, R. L. Barbour, �??Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,�?? Appl. Opt. 9, 6466-6486 (2000)
[CrossRef]

IEEE Trans. Med. Imag.

A. H. Hielscher, A. D. Klose, K. M. Hanson, �??Gradient-Based Iterative Image-Reconstruction Scheme for Time-Resolved Optical Tomography,�?? IEEE Trans. Med. Imag. 18, 262-271 (1999)
[CrossRef]

J. Opt. Soc. Am. A

J. Quantum Spectrosc. Radiat. Transfer

A. D. Klose and A. H. Hielscher, �??Optical tomography using the time-independent equation of radiative transfer �?? Part 2: inverse model,�?? J. Quant. Spectrosc. Radiat. Transfer 72, 715-732 (2002)
[CrossRef]

Med. Phys.

K. D. Paulsen and H. Jiang, �??Spatially varying optical property reconstruction using a finite element diffusion equation approximation,�?? Med. Phys. 22, 691-701 (1995)
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D.T. Delpy, �??A finite element approach for modeling photon transport in tissue,�?? Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Ph. D thesis

F. E. W. Schmidt, Development of a Time-Resolved Optical Tomography System for Neonatal Brain Imaging, Ph. D thesis (1999), University College London

Ph. D. Thesis

Y. Pei, Optical Tomographic Imaging Using the Finite Element Method, Ph. D. Thesis (1999), Polytechnic University.

I. W. Kwee, Towards a Bayesian Framework for Optical Tomography, Ph. D. Thesis (1999), University College London.

Other

S. G. Nash, A. Sofer, Linear and nonlinear programming(McGraw-Hill, New York, 1996)

A Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chap. 9

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Figures (3)

Fig. 1.
Fig. 1.

Reconstructed images after several iterations using conjugate gradient method (col. 1) and weighted steepest descent method with different weighting factors (col. 2), geometry and mesh of the simulation, target image, and the objective function E as a function of weighting factor (col. 3)

Fig. 2.
Fig. 2.

Target image (col. 1), reconstructed images after 100 iterations using CG method (col. 2), and WSD method with optimal weighting factor (col. 3). In all cases, the top image is µ a , and the bottom image is µ’ s .

Fig. 3.
Fig. 3.

Simulation results for multiple targets that are located with different depth. (a) target image. (b) reconstruction result using conventional CG method after 100 iterations. (c) reconstruction result using one step of WSD method and (d) final result using another WSD step.

Tables (2)

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Table 1. Optical parameters of the circular test object

Tables Icon

Table 2 Summaries of the results for the three simulation cases

Equations (12)

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· [ D ( r ) ∇Φ ( r ) ] μ a ( r ) Φ ( r ) = δ ( r r s ) , r Ω
Γ ( ξ ) = D ( ξ ) n ̂ · Φ ( ξ )
E = 1 2 j = 1 S i = 1 M j ( ( Γ j , i ) me ( Γ j , i ) c ) 2
z = E = J T b
D m * = el i , j ( K el * ) i , j ( K el ) i , j D m
d = Z Z 2
A = [ a 11 a 22 0 a ii 0 a NN ]
a ii = L i β , { i = 1 , 2 , , N TOT β 0 }
minimize Z T · d
subject to d T · A · d 1
d = A 1 · z ( Z T · A 1 · Z ) 0.5
· ( c u ) + au = f

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