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Coleman, Thomas F.; Liu, Jianguo; Yuan, Wei

doi:10.1023/a:1008730909894

Cited by 8 publications

(1 citation statement)

References 12 publications

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“…First we replace the ALM scheme with an all-at-once reduced Hessian SQP scheme (rSQP). The SQP scheme, which has been extensively studied in other fields [41][42][43][44][45][46], has the advantage that a much smaller number of convergence parameters have to be preset. In addition, many instability issues inherent to the ALM approach can be avoided that relate to the choice of a penalty parameter, the accuracy of a Lagrange multiplier and the solution unboundness [39].…”

Section: Introductionmentioning

confidence: 99%

A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer

Kim

Hielscher

2008

Inverse Problems

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It is well acknowledged that transport-theory-based reconstruction algorithm can provide the most accurate reconstruction results especially when small tissue volumes or high absorbing media are considered. However, these codes have a high computational burden and are often only slowly converging. Therefore, methods that accelerate the computation are highly desirable. To this end, we introduce in this work a partial-differential-equation (PDE) constrained approach to optical tomography that makes use of an all-at-once reduced Hessian sequential quadratic programming (rSQP) scheme. The proposed scheme treats the forward and inverse variables independently, which makes it possible to update the radiation intensities and the optical coefficients simultaneously by solving the forward and inverse problems, all at once. We evaluate the performance of the proposed scheme with numerical and experimental data, and find that the rSQP scheme can reduce the computation time by a factor of 10-25, as compared to the commonly employed limited memory BFGS method. At the same time accuracy and robustness even in the presence of noise are not compromised.

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