TY - JOUR
T1 - PDE-constrained fluorescence tomography with the frequency-domain equation of radiative transfer
AU - Kim, Hyun Keol
AU - Hwan Lee, Jong
AU - Hielscher, Andreas H.
N1 - Funding Information:
Manuscript received September 25, 2009; accepted November 1, 2009. Date of publication March 22, 2010; date of current version August 6, 2010. This work was supported in part by the National Cancer Institute under Grant NCI-4R33CA118666 and Grant NCI-U54CA126513-039001 at the National Institutes of Health. The work of A. H. Hielscher was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases, the National Heart, Lung, and Blood Institute, the National Institute for Biomedical Imaging and Bioengineering, the National Cancer Institute, the Whitaker Foundation for Biomedical Engineering, and the New York State Office of Science, Technology, and Academic Research.
PY - 2010/7
Y1 - 2010/7
N2 - We present the first fluorescence tomography algorithm that is based on a partial differential equation (PDE) constrained approach. PDE methods have been increasingly employed in many numerical applications, as they often lead to faster and more robust solutions of many inverse problems. In particular, we use a sequential quadratic programming (SQP) method, which allows solving the two forward problems in fluorescence tomography (one for the excitation and one for the emission radiances) and one inverse problem (for recovering the spatial distribution of the fluorescent sources) simultaneously by updating both forward and inverse variables in simultaneously at each of iteration of the optimization process. We evaluate the performance of this approach with numerical and experimental data using a transport-theory frequency-domain algorithm as forward model for light propagation in tissue. The results show that the PDE-constrained approach is computationally stable and accelerates the image reconstruction process up to a factor of 15 when compared to commonly employed unconstrained methods.
AB - We present the first fluorescence tomography algorithm that is based on a partial differential equation (PDE) constrained approach. PDE methods have been increasingly employed in many numerical applications, as they often lead to faster and more robust solutions of many inverse problems. In particular, we use a sequential quadratic programming (SQP) method, which allows solving the two forward problems in fluorescence tomography (one for the excitation and one for the emission radiances) and one inverse problem (for recovering the spatial distribution of the fluorescent sources) simultaneously by updating both forward and inverse variables in simultaneously at each of iteration of the optimization process. We evaluate the performance of this approach with numerical and experimental data using a transport-theory frequency-domain algorithm as forward model for light propagation in tissue. The results show that the PDE-constrained approach is computationally stable and accelerates the image reconstruction process up to a factor of 15 when compared to commonly employed unconstrained methods.
KW - Fluorescence tomography
KW - frequency-domain equation of radiative transfer (ERT)
KW - partial differential equation (PDE) constrained optimization
KW - sequential quadratic programming (SQP)
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U2 - 10.1109/JSTQE.2009.2038112
DO - 10.1109/JSTQE.2009.2038112
M3 - Article
AN - SCOPUS:77955509981
SN - 1077-260X
VL - 16
SP - 793
EP - 803
JO - IEEE Journal on Selected Topics in Quantum Electronics
JF - IEEE Journal on Selected Topics in Quantum Electronics
IS - 4
M1 - 5437173
ER -