• Corpus ID: 246210247

The inverse Rytov series for diffuse optical tomography

@inproceedings{Machida2022TheIR,
  title={The inverse Rytov series for diffuse optical tomography},
  author={Manabu Machida},
  year={2022}
}
The Rytov approximation is known in near-infrared spectroscopy including diffuse optical tomography. In diffuse optical tomography, the Rytov approximation often gives better reconstructed images than the Born approximation. Although related inverse problems are nonlinear, the Rytov approximation is almost always accompanied by the linearization of nonlinear inverse problems. In this paper, we will develop nonlinear reconstruction with the inverse Rytov series. By this, linearization is not… 

References

SHOWING 1-10 OF 28 REFERENCES
Higher order (nonlinear) diffraction tomography: Inversion of the Rytov series
Nonlinear tomographic reconstruction algorithms are developed for inversion of data measured in scattering experiments in which the complex phase of the wavefields is modeled by an arbitrarily large
Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas.
TLDR
A solution to the inverse scattering problem for diffuse light is obtained in the form of a functional series expansion of the pseudoinverse of the linearized forward-scattering operator and leads to the linear inversion formulas that have been reported previously.
On the convergence of the Born series in optical tomography with diffuse light
We provide a simple sufficient condition for the convergence of the Born series in the forward problem of optical diffusion tomography. The Born series considered in this paper is an expansion of
Modified forward and inverse Born series for the Calderon and diffuse-wave problems
We propose a new direct reconstruction method based on series inversion for Electrical Impedance Tomography (EIT) and the inverse scattering problem for diffuse waves. The standard Born series for
Nonlinear inverse scattering and three-dimensional near-field optical imaging
The nonlinear inverse scattering problem for electromagnetic fields with evanescent components is considered. A solution to this problem is obtained in the form of a functional series expansion. The
A family of approximations spanning the Born and Rytov scattering series.
TLDR
The linearized hybrid approximation is derived and demonstrated by simulations of inverse scattering off of uniform circular cylinders, where it is shown that the hybrid approximation achieves smaller error than either the Born or Rytov approximations alone.
Symmetries, inversion formulas, and image reconstruction for optical tomography.
TLDR
The effects of sampling and limited data are analyzed for several different experimental modalities, and computationally efficient reconstruction algorithms are obtained that are suitable for the reconstruction of images from very large data sets.
Restarted inverse Born series for the Schrödinger problem with discrete internal measurements
Convergence and stability results for the inverse Born series (Moskow and Schotland 2008 Inverse Problems 24 065005) are generalized to mappings between Banach spaces. We show that by restarting the
Renormalization group interpretation of the Born and Rytov approximations.
  • E. Kirkinis
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2008
TLDR
It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart.
Optical tomography in medical imaging
We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to the
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