Application of integral transform algorithms to high-resolution reconstruction of tissue inhomogeneities in medical diffuse optical tomography

Abstract

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.

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

“…Let us consider a common 2D geometry for DOT, when sources and receivers lie around the boundary of a circular object at equal step angles. Our investigations [11][12][13][14][15] show that by choosing the optimal values of the time-gating delay of receivers, the length of the middle segment of the broken PAT may be greatly longer than the first and the end ones. Moreover, the time-gating delays for different source-receiver pairs can be chosen so that the lengths of the outer segments for all broken-line approximations of the PATs are equal.…”

“…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][5][6][7][8][9][10][11][12][13][14][15][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 source to a receiver in a form admitting probabilistic interpretation.…”

“…As a result, the PAT method can be implemented as a "one-step" technique with the use of fast algorithms of projection computed tomography and can considerably save the computation time. Our experience shows that not only the algebraic techniques [11,16] but also the real-time filtered backprojection algorithm (FBP) [12][13][14][15] can be successfully applied to reconstruct the internal region of the object, where the PATs tend to the straight line. The shortcoming of the PAT method is that it reconstructs the tomograms blurred due to averaging over spatial distributions of photons which form the signal measured by the receiver.…”

“…The shortcoming of the PAT method is that it reconstructs the tomograms blurred due to averaging over spatial distributions of photons which form the signal measured by the receiver. To improve the spatial resolution, we have tried to use FBP with special filtration of shadows (Vainberg [12][13][14][15] or hybrid Vainberg-Butterworth 2 EURASIP Journal on Advances in Signal Processing filtration [15]). This algorithm gives a 20%-gain in resolution but does not correctly restore the inhomogeneity profile as the averaging kernel is not taken into account.…”

Methods for Postprocessing in Single-Step Diffuse Optical Tomography

“…the problem of radiation propagation through tissue is solved numerically many times and at each step of linearization it is necessary to adjust the matrix of the system of algebraic equations that describe the discrete reconstruction model. As shown in our earlier papers (Kalintsev et al, 2005;Konovalov et al, 2003;2006b;2007a;2007b;Lyubimov et al, 2002;, there exists a unique opportunity to make the reconstruction procedure much faster by changing over in equation (1) from volume integration to integration along an effective trajectory from source to receiver. The photon average trajectory method (PAT method) we have developed finds such a trajectory using a probabilistic interpretation of light energy transfer by photons from source to receiver.…”