Vadim A. Markel

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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 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)
We continue our study of the inverse scattering problem for diffuse light. In particular, we derive inversion formulas for this problem that are based on the functional singular-value decomposition of the linearized forward-scattering operator in the slab, cylindrical, and spherical geometries. Computer simulations are used to illustrate our results in(More)
We consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean-free path is on the order of the system size. It is shown that a tomographic imaging technique can be devised which is based on the assumption of single scattering and utilizes a generalization of the Radon transform which we refer to as the broken-ray(More)
We report theory and numerical simulations that demonstrate the feasibility of simultaneous reconstruction of the three-dimensional scattering and absorption coefficients of a mesoscopic system using angularly resolved measurements of scattered light. Image reconstruction is based on the inversion of a generalized (broken ray) Radon transform relating the(More)
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)
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)
In recent years, optical tomography (OT) of highly scattering biological samples has increasingly relied on noncontact CCD-based imaging devices that can record extremely large data sets, with up to 10(9) independent measurements per sample. Reconstruction of such data sets requires fast algorithms. The latter have been developed and applied experimentally(More)