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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)

- Zheng-Min Wang, George Y Panasyuk, Vadim A Markel, John C Schotland
- Optics letters
- 2005

We report the first experimental test of an analytic image reconstruction algorithm for optical tomography with large data sets. Using a continuous-wave optical tomography system with 10(8) source-detector pairs, we demonstrate the reconstruction of an absorption image of a phantom consisting of a highly scattering medium containing absorbing… (More)

A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(ˆ s, ˆ s) with the constraint that it depends only on the angle between the angular variablesˆs andˆs. This assumption corresponds to… (More)

The radiative transport equation is solved in the three-dimensional slab geometry by means of the method of rotated reference frames. In this spectral method, the solution is expressed in terms of analytical functions such as spherical harmonics and Wigner d-functions. In addition, the eigenvalues and eigenvectors of a tridiagonal matrix and certain… (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

- Vadim A Markel
- Journal of the Optical Society of America. A…
- 2016

This tutorial is devoted to the Maxwell Garnett approximation and related theories. Topics covered in this first, introductory part of the tutorial include the Lorentz local field correction, the Clausius-Mossotti relation and its role in the modern numerical technique known as the discrete dipole approximation, the Maxwell Garnett mixing formula for… (More)

- Han Y Ban, David R Busch, +5 authors Arjun G Yodh
- Journal of biomedical optics
- 2013

Diffuse optical tomography (DOT) has been employed to derive spatial maps of physiologically important chromophores in the human breast, but the fidelity of these images is often compromised by boundary effects such as those due to the chest wall. We explore the image quality in fast, data-intensive analytic and algebraic linear DOT reconstructions of… (More)

- 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.