Nonlinear multigrid algorithms for Bayesian optical diffusion tomography

Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a difficult nonlinear inverse problem. Bayesian approaches are ef...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 10; no. 6; pp. 909 - 922
Main Authors: Jong Chul Ye, Bouman, C.A., Webb, K.J., Millane, R.P.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.06.2001
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Artificial intelligence
Bayesian analysis
Bayesian methods
Computation
Computer science; control theory; systems
Diffusion
Exact sciences and technology
Image processing
Image reconstruction
Imaging
Information, signal and communications theory
Inverse problems
Light scattering
Multigrid methods
Nonlinear optics
Nonlinearity
Optical imaging
Optical modulation
Optical scattering
Optimization
Pattern recognition. Digital image processing. Computational geometry
Signal processing
Telecommunications and information theory
Tomography
Bayes estimation
Image processing
Multigrid
A posteriori estimation
Tomography
Non linear processing
Optical scattering
Algorithm
Multiresolution analysis
Medical application
Optimization
Image reconstruction
ISSN:1057-7149, 1941-0042
Online Access:Get full text
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Summary:Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a difficult nonlinear inverse problem. Bayesian approaches are effective, but are computationally expensive, especially for three-dimensional (3-D) imaging. This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of nonquadratic optimization problems. This multigrid method is applied to compute the maximum a posteriori (MAP) estimate of the reconstructed image in the optical diffusion tomography problem. The proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality.
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ISSN:1057-7149
1941-0042
DOI:10.1109/83.923287