Space-Varying Iterative Restoration of Diffuse Optical Tomograms Reconstructed by the Photon Average Trajectories Method

Abstract

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 gain in spatial resolution can be obtained.