Direct Sampling Method for Diffusive Optical Tomography

@article{Chow2015DirectSM,
  title={Direct Sampling Method for Diffusive Optical Tomography},
  author={Yat Tin Chow and Kazufumi Ito and Keji Liu and Jun Zou},
  journal={SIAM J. Sci. Comput.},
  year={2015},
  volume={37}
}
In this work, we are concerned with the diffusive optical tomography (DOT) problem in the case when only one or two pairs of Cauchy data is available. We propose a simple and efficient direct sampling method (DSM) to locate inhomogeneities inside a homogeneous background and solve the DOT problem in both full and limited aperture cases. This new method is easy to implement and less expensive computationally. Numerical experiments demonstrate its effectiveness and robustness against noise in the… Expand
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References

SHOWING 1-10 OF 79 REFERENCES
A direct sampling method to an inverse medium scattering problem
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneousExpand
New imaging algorithm in diffusion tomography
A novel imaging algorithm for diffusion/optical tomography is presented for the case of the time dependent diffusion equation. Numerical tests are conducted for ranges of parameters realistic forExpand
Nonlinear multigrid algorithms for Bayesian optical diffusion tomography
TLDR
This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of nonquadratic optimization problems and dramatically reduces the required computation and improves the reconstructed image quality. Expand
A fast and accurate imaging algorithm in optical/diffusion tomography
An n-dimensional (n = 2,3) inverse problem for the parabolic/diffusion equation , , , is considered. The problem consists of determining the function a(x) inside of a bounded domain given the valuesExpand
A reconstruction algorithm for ultrasound-modulated diffuse optical tomography
The aim of this paper is to develop an efficient reconstruction algorithm for ultrasound-modulated diffuse optical tomography. In diffuse optical imaging, the resolution is in general low. ByExpand
Multigrid inversion algorithms with applications to optical diffusion tomography
In this paper, we propose a general framework for nonlinear multigrid inversion applicable to any inverse problem in which the forward model can be naturally represented at differing resolutions. InExpand
Reconstruction and stability in acousto-optic imaging for absorption maps with bounded variation ☆
The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acousto-optic data absorption distributions with bounded variation. The paperExpand
Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media.
TLDR
The image of an object hidden in highly scattering media was reconstructed using a fast, noise-resistant algorithm newly applied to diffusion tomography, and an inverse scattering algorithm with nonuniform regularization achieves rapid inversion convergence. Expand
Sensitivity to prior knowledge in optical tomographic reconstruction
The performance of reconstruction algorithms for near-IR optical tomography depends critically on the accuracy of the forward model used to evaluate the closeness of a given solution to that mostExpand
Globally accelerated reconstruction algorithm for diffusion tomography with continuous-wave source in an arbitrary convex shape domain.
TLDR
A new numerical imaging algorithm is presented for reconstruction of optical absorption coefficients from near-infrared light data with a continuous-wave source that solves the inverse problem through solution of a boundary-value problem for a Volterra-type integral partial differential equation. Expand
...
1
2
3
4
5
...