TY - JOUR
A2 - Gandarias, Maria
AU - Favennec, Y.
AU - Dubot, F.
AU - Le Hardy, D.
AU - Rousseau, B.
AU - Rousse, D. R.
PY - 2016
DA - 2016/03/29
TI - Space-Dependent Sobolev Gradients as a Regularization for Inverse Radiative Transfer Problems
SP - 3543571
VL - 2016
AB - Diffuse optical tomography problems rely on the solution of an optimization problem for which the dimension of the parameter space is usually large. Thus, gradient-type optimizers are likely to be used, such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, along with the adjoint-state method to compute the cost function gradient. Usually, the L2-inner product is chosen within the extraction procedure (i.e., in the definition of the relationship between the cost function gradient and the directional derivative of the cost function) while alternative inner products that act as regularization can be used. This paper presents some results based on space-dependent Sobolev inner products and shows that this method acts as an efficient low-pass filter on the cost function gradient. Numerical results indicate that the use of Sobolev gradients can be particularly attractive in the context of inverse problems, particularly because of the simplicity of this regularization, since a single additional diffusion equation is to be solved, and also because the quality of the solution is smoothly varying with respect to the regularization parameter.
SN - 1024-123X
UR - https://doi.org/10.1155/2016/3543571
DO - 10.1155/2016/3543571
JF - Mathematical Problems in Engineering
PB - Hindawi Publishing Corporation
KW -
ER -