A Primal-Dual Reconstruction Algorithm For Fluorescence And Bioluminescence Tomography

Jean-Charles Baritaux, Michaël Unser
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa, 2011
Article de conférence

Résumé

We introduce a new primal-dual reconstruction algorithm for fluorescence and bioluminescence tomography. As often in optical tomography, image reconstruction is performed by optimizing a multi-term convex cost function. Current reconstruction methods employed in the field are usually limited to cost functions with a smooth data fidelity term; quadratic in general. In addition, the use of a composite regularization term (a sum of multiple terms) requires a substantial adaptation of these methods. Typically one would have to solve a subproblem via a primal-dual method at each iteration. The primaldual scheme presented here is designed to handle directly cost functions composed of multiple, possibly non-smooth, terms. This allows more freedom for the design of tailored cost functions leading to enhanced reconstructions. We illustrate the method on two cases. First, we use a cost function composed of l(1) fidelity and regularization terms. We compare to the reconstructions obtained with the quadratic fidelity counterpart. Second, we employ a cost function composed of three terms : l(1) for data fidelity, total-variation plus (2,1)-mixed norms for regularization.

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https://infoscience.epfl.ch/record/178452?ln=fr

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Publications associées (3)

A Primal-Dual Reconstruction Algorithm for Fluorescence and Bioluminescence Tomography

Jean-Charles Baritaux, Michaël Unser

We introduce a new primal-dual reconstruction algorithm for fluorescence and bioluminescence tomography. As often in optical tomography, image reconstruction is performed by optimizing a multi-term convex cost function. Current reconstruction methods employed in the field are usually limited to cost functions with a smooth data fidelity term; quadratic in general. In addition, the use of a composite regularization term (a sum of multiple terms) requires a substantial adaptation of these methods. Typically one would have to solve a subproblem via a primal-dual method at each iteration. The primal-dual scheme presented here is designed to handle directly cost functions composed of multiple, possibly non-smooth, terms. This allows more freedom for the design of tailored cost functions leading to enhanced reconstructions. We illustrate the method on two cases. First, we use a cost function composed of

ℓ _{ 1 }

fidelity and regularization terms. We compare to the reconstructions obtained with the quadratic fidelity counterpart. Second, we employ a cost function composed of three terms :

ℓ _{ 1 }

for data fidelity, total-variation plus (2,1)-mixed norms for regularization.

IEEE2011

Chargement

Reconstruction algorithms for Optical Diffuse Tomography (ODT) rely heavily on fast and accurate forward models. Arbitrary geometries and boundary conditions need to be handled rigorously since they are the only input to the inverse problem. From this perspective, Finite Element Methods (FEM) are good candidates to implement a forward model. However, these methods require to mesh the domain of interest, which is impractical on a routine basis. The other downside of the FEM is that the basis functions are often not compatible with the ones used for solving the inverse problem, which typically have less degrees of freedom. In this work, we tackle the 2D problem, and propose a forward model that uses a mesh-free discretization based on linear B-Splines. It combines the advantages of the FEM, while offering a fast and much simpler way of handling complex geometries. Another motivation for this work is that the underlying B-spline model is equally suitable for the subsequent reconstruction part of the process (solving the inverse problem). In particular, it is compatible with wavelets and multiresolution-type signal representations.

IEEE2008

Chargement

, , ,

Optical tomographic imaging requires an accurate forward model as well as regularization to mitigate missing-data artifacts and to suppress noise. Nonlinear forward models can provide more accurate interpretation of the measured data than their linear counterparts, but they generally result in computationally prohibitive reconstruction algorithms. Although sparsity-driven regularizers significantly improve the quality of reconstructed image, they further increase the computational burden of imaging. In this paper, we present a novel iterative imaging method for optical tomography that combines a nonlinear forward model based on the beam propagation method (BPM) with an edge-preserving three-dimensional (3-D) total variation (TV) regularizer. The central element of our approach is a time-reversal scheme, which allows for an efficient computation of the derivative of the transmitted wave-field with respect to the distribution of the refractive index. This time-reversal scheme together with our stochastic proximal-gradient algorithm makes it possible to optimize under a nonlinear forward model in a computationally tractable way, thus enabling a high-quality imaging of the refractive index throughout the object. We demonstrate the effectiveness of our method through several experiments on simulated and experimentally measured data.

2016

Chargement

A Primal-Dual Reconstruction Algorithm for Fluorescence and Bioluminescence Tomography

Jean-Charles Baritaux, Michaël Unser

We introduce a new primal-dual reconstruction algorithm for fluorescence and bioluminescence tomography. As often in optical tomography, image reconstruction is performed by optimizing a multi-term convex cost function. Current reconstruction methods employed in the field are usually limited to cost functions with a smooth data fidelity term; quadratic in general. In addition, the use of a composite regularization term (a sum of multiple terms) requires a substantial adaptation of these methods. Typically one would have to solve a subproblem via a primal-dual method at each iteration. The primal-dual scheme presented here is designed to handle directly cost functions composed of multiple, possibly non-smooth, terms. This allows more freedom for the design of tailored cost functions leading to enhanced reconstructions. We illustrate the method on two cases. First, we use a cost function composed of

ℓ _{ 1 }

fidelity and regularization terms. We compare to the reconstructions obtained with the quadratic fidelity counterpart. Second, we employ a cost function composed of three terms :

ℓ _{ 1 }

for data fidelity, total-variation plus (2,1)-mixed norms for regularization.

IEEE2011