<title>High-resolution restoration of diffuse optical images reconstructed by the photon average trajectories method</title>

Abstract

The possibility of improving the spatial resolution of diffuse optical images 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 (DOT) is reduced to solution of 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. In our recent works we have shown that the application of the backprojection algorithms with special filtration of shadows allows a 20%-gain in spatial resolution to be obtained. But the shortcoming of the backprojection algorithm is that they can not reconstruct accurately the object regions located close to the boundary. In the present paper we consider alternative approach to improve the spatial reconstruction, which may be applied to images reconstructed with the use of algebraic techniques. It is based on post-reconstruction restoration of images blurred due to averaging over spatial distributions of photons, which form the signal measured by the receiver. We suggest a spatially invariant blurring model to restore local regions of a diffuse image with the use of standard deconvolution algorithms. Two iterative non-linear algorithms: the maximum-likelihood algorithm and the Lucy-Richardson algorithm are considered. It is shown that both of them allow the spatial resolution to be improved. The effect of the improvement is identical to that obtained with the use of the backprojection algorithms.