Space-Varying Iterative Restoration of Diffuse Optical Tomograms Reconstructed by the Photon Average Trajectories Method
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Research Article Space-Varying Iterative Restoration of Diffuse Optical Tomograms Reconstructed by the Photon Average Trajectories Method Alexander B. Konovalov,1 Vitaly V. Vlasov,1 Olga V. Kravtsenyuk,2 and Vladimir V. Lyubimov3 1 Russian
Federal Nuclear Centre, Institute of Technical Physics, P.O. Box 245, Snezhisk Chelyabinsk Region 456770, Russia 2 Institute of Electronic Structure and Laser, Foundation for Research and Technology – Hellas, P.O. Box 1527, Vassilika Vouton, Heraklion 71110, Greece 3 Research Institute for Laser Physics, 12 Birzhevaya Lin, Saint Petersburg 199034, Russia Received 2 February 2006; Revised 2 August 2006; Accepted 29 October 2006 Recommended by Lisimachos Paul Kondi The possibility of improving the spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT) method is substantiated. The PAT method recently presented by us is based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT). The inverse problem of diffuse optical tomography is reduced to a solution of an integral equation with integration along a conditional PAT. As a result, the conventional algorithms of projection computed tomography can be used for fast reconstruction of diffuse optical images. The shortcoming of the PAT method is that it reconstructs the images blurred due to averaging over spatial distributions of photons which form the signal measured by the receiver. To improve the resolution, we apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small subregions of the image domain. Two iterative algorithms for solving a system of linear algebraic equations, the conjugate gradient algorithm for least squares problem and the modified residual norm steepest descent algorithm, are used for deblurring. It is shown that a 27% gain in spatial resolution can be obtained. Copyright © 2007 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
The main problem of medical diffuse optical tomography (DOT) is the low spatial resolution due to multiple light scattering, which causes photons to propagate diffusely in a tissue. To reconstruct diffuse optical tomograms with best resolution, “well-designed” methods such as Newton-like and gradient-like ones [1–3], which use exact forward models, are generally applied. These methods belong to a class of a so-called “multistep” techniques, as the weighting matrix of equation system is updated on each iteration of the solution approximation. They require computation time not less than a few minutes for 2D image reconstruction and consequently are inapplicable for real-time medical explorations. Over the past few years, we have presented a new DOT method [4–16] based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT). The essence of this concept is in rep-
resenting the process of the photon energy transport from a sou
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