19 May 2006 Diffuse optical tomogram restoration with spatially variant point spread function
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The possibility of improving the spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT) method is substantiated. The PAT method 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 standard filtered back projection algorithm can be used for fast reconstruction of diffuse optical tomograms. 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, I apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small sub-regions 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 the restoration procedure enhances the tomogram profiles and allows an obvious gain in spatial resolution to be obtained.
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Alexander B. Konovalov, Alexander B. Konovalov, } "Diffuse optical tomogram restoration with spatially variant point spread function", Proc. SPIE 6257, ICONO 2005: Nonlinear Laser Spectroscopy, High Precision Measurements, and Laser Biomedicine and Chemistry, 62570Q (19 May 2006); doi: 10.1117/12.678374; https://doi.org/10.1117/12.678374

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