The applicability of the transform algorithms generally used in projection computed tomography is substantiated for the case of medical diffuse optical tomography (DOT). To reconstruct tissue optical inhomogeneities, a new method based on a concept of an average statistical trajectory for transfer of light energy (photon average trajectory, PAT) is proposed. By this method, the inverse problem of DOT is reduced to solution of integral equation with integration along a PAT. Within the internal zone of the object, remote well away from the boundaries, PATs tend to a straight line, and standard integral algorithms based on the inverse Radon transform may be used to restore diffuse optical images. To demonstrate the capabilities of the PAT method, a numerical experiment on cross-sectional reconstruction of cylindrical strongly scattering objects with absorbing inhomogeneities has been conducted. To solve the DOT inverse problem, two filtered backprojection algorithms (of Radon and of Vainberg) were used. The reconstruction results are compared with those obtained by a well-known software package for temporal optical absorption and scattering tomography, based on multiple solution of diffusion equation. It is shown that the PAT method using the Vainberg algorithm allows reconstruction of tissue optical structure with a 20%-gain in spatial resolution.
The applicability of backprojection algorithms of filtered shadows that have been earlier developed for computer tomography is shown for the case of optical tomography of strongly scattering media. This opportunity is based on the presence of a long rectilinear part in the approximation of the statistical Photon Average Trajectories of photons propagating through the scattering medium. The results of numerical experiments showed that the quality of reconstruction using filtered backprojection algorithms do not surrender to that for multi-iterative algorithms, at much shorter reconstruction time.
The applicability of transform algorithms generally used in projection-computed tomography is substantiated for the case of medical optical diffusion tomography (ODT). To reconstruct tissue optical inhomogeneities, a new method based on a concept of an average statistical trajectory for transfer of light energy [photon average trajectory (PAT)] is proposed. By this method, the inverse problem of ODT is reduced to a solution of an integral equation with integration along a PAT. Within the internal zone of the object, well away from the boundaries, PATs tend to a straight line, and standard integral algorithms based on the inverse Radon transform may be used to restore diffuse optical images. To demonstrate the capabilities of the PAT method, a numerical experiment on cross sectional reconstruction of cylindrical strongly scattering objects with lowcontrast absorbing inhomogeneities is conducted. To solve the timedomain ODT inverse problem, two filtered backprojection algorithms (of Radon and Vainberg) are used. The reconstruction results are compared with those obtained by a well-known software package for temporal optical absorption and scattering tomography, based on multiple solutions of a diffusion equation. It is shown that in important cases of low-contrast absorbing inhomogeneities, the PAT method using the Vainberg algorithm allows reconstruction of tissue optical inhomogeneities with a 20% gain in spatial resolution.
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