Optical tomography reconstruction algorithm with the finite element method: An optimal approach with regularization tools

Balima, O.; Favennec, Yann; Rousse, Daniel R.

doi:10.1016/j.jcp.2013.04.043

Cited by 18 publications

(16 citation statements)

References 44 publications

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“…As the inverse problem is ill-posed, regularization procedure is compulsory. Different regularization tools were investigated in this work: parameterization of the control space, Tikhonov penalization and Sobolev gradients, [7]. The paper will be the first to present the resolution of the inverse problem.…”

Section: Retrieval Of the Radiative Propertiesmentioning

confidence: 99%

Infrared tomography: towards a novel methodology to investigate the volumetric radiative properties of heterogeneous materials

Rousseau¹,

Favennec²,

Guévelou³

et al. 2014

Proceedings of the 2014 International Conference on Quantitative InfraRed Thermography

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Knowledge of the volumetric radiative properties of heterogeneous semi-transparent materials is of crucial interest to accurately quantify the propagation of radiative energy carried through them. When the materials exhibit a complex texture, the determination of their radiative properties remains tricky. Experimental and/or numerical methodologies aiming to finely retrieve the spatial dependence of these properties are at their first step of development. The research proposed in this paper uses optical tomography and specific numerical approaches to solve the inherent inverse problem to solve this issue.

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Section: Retrieval Of the Radiative Propertiesmentioning

confidence: 99%

Infrared tomography: towards a novel methodology to investigate the volumetric radiative properties of heterogeneous materials

Rousseau¹,

Favennec²,

Guévelou³

et al. 2014

Proceedings of the 2014 International Conference on Quantitative InfraRed Thermography

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“…In this context, near-infrared light is used in order to take advantage of the so-called therapeutic window (600-900 nm) in which tissues have low absorption. According to the application, RTE has to be considered as forward model [14][15][16][17][18][19], diffuse approximation (DA) may be applied [8,12,[20][21][22][23], or hybrid model is employed [24][25][26][27][28]. This paper deals with two very different forward models, namely, the bidimensional steady-state RTE and the threedimensional frequency DA, in order to gauge the potential ability of the introduced regularization with the different models.…”

Section: Introductionmentioning

confidence: 99%

Space-Dependent Sobolev Gradients as a Regularization for Inverse Radiative Transfer Problems

Favennec

Dubot

Hardy

et al. 2016

Mathematical Problems in Engineering

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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 2 -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.

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“…The methods employed to solve this problem include the non-linear conjugate-gradient method [3], Gauss-Newton based methods [4][5][6][7], the L-BFGS method [8][9][10][11][12], shape-based reconstruction method [13,14] or, in a Bayesian framework, the approximation error method [15,16]. Regarding the first three listed methods, some problems remain to be overcome such as the stability with respect to the initial guesses and the blurring effect of the reconstructed images due to the need for relatively strong regularization tools [17,14].…”

Section: Introductionmentioning

confidence: 99%

“…Comparisons with other methods found in the literature such as the Gauss-Newton method is out of the scope of the paper. However, let us point-out that the L-BFGS method has proven its worth in the field of the optical tomography as shown by the following papers [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A wavelet multi-scale method for the inverse problem of diffuse optical tomography

Dubot

Favennec

Rousseau

et al. 2015

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper deals with the estimation of optical property distributions of participating media from a set of light sources and sensors located on the boundaries of the medium. This is the so-called diffuse optical tomography problem. Such a non-linear ill-posed inverse problem is solved through the minimization of a cost function which depends on the discrepancy, in a least-square sense, between some measurements and associated predictions. In the present case, predictions are based on the diffuse approximation model in the frequency domain while the optimization problem is solved by the L-BFGS algorithm. To cope with the local convergence property of the optimizer and the presence of numerous local minima in the cost function, a wavelet multi-scale method associated with the L-BFGS method is developed, implemented, and validated. This method relies on a reformulation of the original inverse problem into a sequence of sub-inverse problems of different scales using wavelet transform, from the largest scale to the smallest one. Numerical results show that the proposed method brings more stability with respect to the ordinary L-BFGS method and enhances the reconstructed images for most of initial guesses of optical properties.

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Optical tomography reconstruction algorithm with the finite element method: An optimal approach with regularization tools

Cited by 18 publications

References 44 publications

Infrared tomography: towards a novel methodology to investigate the volumetric radiative properties of heterogeneous materials

Infrared tomography: towards a novel methodology to investigate the volumetric radiative properties of heterogeneous materials

Space-Dependent Sobolev Gradients as a Regularization for Inverse Radiative Transfer Problems

A wavelet multi-scale method for the inverse problem of diffuse optical tomography

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