Optical tomography as a PDE-constrained optimization problem

@article{Abdoulaev2005OpticalTA,
  title={Optical tomography as a PDE-constrained optimization problem},
  author={Gassan Abdoulaev and Kui Ren and Andreas H. Hielscher},
  journal={Inverse Problems},
  year={2005},
  volume={21},
  pages={1507 - 1530}
}
We report on the implementation of an augmented Lagrangian approach for solving the inverse problems in diffuse optical tomography (DOT). The forward model of light propagation is the radiative transport equation (RTE). The inverse problem is formulated as a minimization problem with the RTE being considered as an equality constraint on the set of ‘optical properties—radiance’ pairs. This approach allows the incorporation of the recently developed technique of PDE-constrained optimization… 

A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer

It is well acknowledged that transport-theory-based reconstruction algorithm can provide the most accurate reconstruction results especially when small tissue volumes or high absorbing media are

A New Numerical Approach to Inverse Transport Equation with Error Analysis

The approach is to decompose the measurements into three components, two out of which encode the information of the two coefficients respectively, and split the optimization problem into two subproblems and use those two components to recover the absorption and scattering coefficients separately.

Three-dimensional optical tomography with the equation of radiative transfer

We report on the derivation and implementation of the first three-dimensional optical tomographic image reconstruction scheme that is based on the time-independent equation of radiative transfer

Adaptive finite element methods for the solution of inverse problems in optical tomography

Optical tomography attempts to determine a spatially variable coefficient in the interior of a body from measurements of light fluxes at the boundary. Like in many other applications in biomedical

Diffuse optical tomographic imaging of biological media by time-dependent parabolic SP(N) equations: a two-dimensional study.

The results suggest the DOT algorithm based on the TD-pSPN model outperforms the DE, and accurately reconstructs optical parameter distributions of biological media both spatially and quantitatively.

Recent Developments in Numerical Techniques for Transport-Based Medical Imaging Methods

The objective of this paper is to review recent developments in numerical reconstruction methods for inverse transport problems in imaging applications, mainly optical tomography, fluorescence

Inverse Optical Tomography through PDE Constrained Optimization L∞

Novel methods of Calculus of Variations in L∞ are utilised to lay the mathematical foundations of FOT, which is posed as a PDE-constrained minimisation problem in Lp and L ∞.

Recent Developments in Numerical Techniques for Transport-Based Medical Imaging Methods

The objective of this paper is to reviewrecent developments in numerical re- construction methods for inverse transport problems in imaging applications, mainly optical tomography, fluorescence
...

References

SHOWING 1-10 OF 76 REFERENCES

Active constrained truncated Newton method for simple-bound optical tomography

  • RoySevick-Muraca
  • Mathematics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2000
The inverse optical imaging problem is formulated as both simple-bound constrained and unconstrained minimization problems in order to illustrate the reduction in computational time and storage associated with constrained image reconstructions and confirms that the physically based, constrained minimization with efficient optimization schemes may offer a more logical approach to the large-scale optical imaging issue.

Frequency Domain Optical Tomography Based on the Equation of Radiative Transfer

Numerical simulations with synthetic data show that the cross-talk between the two optical parameters is significantly reduced in reconstructions based on frequency-domain data as compared to those based on steady-state data.

Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer.

An iterative image reconstruction scheme for optical tomography that is based on the equation of radiative transfer that accurately describes the photon propagation in turbid media without any limiting assumptions regarding the optical properties is reported on.

Three-dimensional optical tomography with the equation of radiative transfer

We report on the derivation and implementation of the first three-dimensional optical tomographic image reconstruction scheme that is based on the time-independent equation of radiative transfer

Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography.

This work presents the underlying concepts in their approach to overcome ill-posedness in optical tomography and shows numerical results that demonstrate how prior knowledge, represented as penalty terms, can improve the reconstruction results.

Gradient-based iterative image reconstruction scheme for time-resolved optical tomography

Numerical studies suggest that intraventricular hemorrhages can be detected using the GIIR technique, even in the presence of a heterogeneous background.

Three-dimensional unconstrained and constrained image-reconstruction techniques applied to fluorescence, frequency-domain photon migration.

The image-reconstruction results confirm that the constrained minimization may offer a more logical approach for the 3-D optical imaging problem than unconstrained optimization.

Application of the finite-element method for the forward and inverse models in optical tomography

The iterative image recovery algorithm described in this paper uses a numerical finite-element solution to the diffusion equation as the photon propagation model to compare the influence of absorbing and scattering inhomogeneities embedded in a homogeneous tissue sample on boundary measurements.

A transport-backtransport method for optical tomography

Optical tomography is modelled by the inverse problem of the time-dependent linear transport equation in n spatial dimensions (n = 2,3). Based on the measurements which consist of some functionals of

Optical diffusion tomography by iterative- coordinate-descent optimization in a Bayesian framework

Numerical results for two-dimensional images show that the Bayesian framework with the new optimization scheme outperforms conventional approaches in both speed and reconstruction quality.
...