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We consider the image reconstruction problem for optical tomography in the transmission geometry. We investigate the effects of sampling and limited data on this inverse problem and derive an explicit inversion which is computationally efficient and stable in the presence of noise. The propagation of near-infrared light in many biological tissues is… (More)

- Vadim A Markel, Joseph A O'Sullivan, John C Schotland
- Journal of the Optical Society of America. A…
- 2003

We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized… (More)

We consider the inverse scattering problem for the radiative transport equation. We show that the linearized form of this problem can be formulated in terms of the inversion of a suitably defined Fourier-Laplace transform. This generalizes a previous result obtained within the diffusion approximation to the radiative transport equation.

- Vadim A. Markel
- 2006

- V A Markel, J C Schotland
- Journal of the Optical Society of America. A…
- 2001

We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. Inversion formulas based on the Fourier-Laplace transform are used to establish the existence and uniqueness of solutions to this problem in planar, cylindrical, and spherical geometries.

- J C Schotland, V A Markel
- Journal of the Optical Society of America. A…
- 2001

We consider the problem of imaging the optical properties of a highly scattering medium probed by diffuse light. An analytic solution to this problem is derived from the singular value decomposition of the forward-scattering operator, which leads to explicit inversion formulas for the inverse scattering problem with diffusing waves. Computer simulations are… (More)

- Vadim A Markel, John C Schotland
- Journal of the Optical Society of America. A…
- 2002

We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. The role of boundary conditions in the derivation of Fourier-Laplace inversion formulas is considered. Boundary conditions of a general mixed type are discussed, with purely absorbing and purely… (More)

- Soren D Konecky, George Y Panasyuk, Kijoon Lee, Vadim Markel, Arjun G Yodh, John C Schotland
- Optics express
- 2008

We use diffuse optical tomography to quantitatively reconstruct images of complex phantoms with millimeter sized features located centimeters deep within a highly-scattering medium. A non-contact instrument was employed to collect large data sets consisting of greater than 10(7) source-detector pairs. Images were reconstructed using a fast image… (More)

- Vadim A Markel, John C Schotland
- Physical review. E, Statistical, nonlinear, and…
- 2004

We consider the image reconstruction problem for optical tomography with diffuse light. The associated inverse scattering problem is analyzed by making use of particular symmetries of the scattering data. The effects of sampling and limited data are analyzed for several different experimental modalities, and computationally efficient reconstruction… (More)

- V A Markel, J C Schotland
- Physical review. E, Statistical, nonlinear, and…
- 2001

We consider the inverse scattering problem for the diffusion equation. A solution to this problem in the form of an explicit inversion formula is derived. Computer simulations are used illustrate our approach in model systems.