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Phys Med Biol. 2005 May 21;50(10):2365-86. Epub 2005 May 5.

Gauss-Newton method for image reconstruction in diffuse optical tomography.

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Department of Computer Science, University College London, Gower Street London WC1E 6BT, UK.


We present a regularized Gauss-Newton method for solving the inverse problem of parameter reconstruction from boundary data in frequency-domain diffuse optical tomography. To avoid the explicit formation and inversion of the Hessian which is often prohibitively expensive in terms of memory resources and runtime for large-scale problems, we propose to solve the normal equation at each Newton step by means of an iterative Krylov method, which accesses the Hessian only in the form of matrix-vector products. This allows us to represent the Hessian implicitly by the Jacobian and regularization term. Further we introduce transformation strategies for data and parameter space to improve the reconstruction performance. We present simultaneous reconstructions of absorption and scattering distributions using this method for a simulated test case and experimental phantom data.

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