Olga V. Kravtsenyuk

Space-varying iterative restoration of diffuse optical tomograms reconstructed by the photon average trajectories method

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.

The photon average trajectory method for One-step diffuse optical tomography: Algebraic reconstruction and postprocessing

The photon average trajectory method reduces the inverse problem of diffuse optical tomography to solution of an integral equation with integration along a curvilinear photon average trajectory. As a result, the discrete reconstruction model with the one-step inversion of a system of linear algebraic equations can be applied. For solving the system, we use the multiplicative algebraic reconstruction technique modified to improve the quality of diffusion tomograms. Space-varying restoration and methods of nonlinear color interpretation are applied for postprocessing. To study the efficiency of proposed methods, a numerical experiment is conducted, where a rectangular scattering object with circular absorbing inhomogeneities is reconstructed over optical projections simulated for the time-domain measurement technique. It is shown that our approach allows reconstructing images with quality close to that of well-designed multi-step algorithms at considerable savings of computational time.

Methods for Postprocessing in Single-Step Diffuse Optical Tomography

The methods of computed tomography – X-ray computed tomography, magnetic resonance imaging, single-photon emission computed tomography, positron emission tomography, ultrasonic reflectivity tomography and others (Webb, 1998) are now widely used in the practice of medical imaging and their importance increasingly grows. These methods allow the real time reproduction and visual analysis of the inner spatial structure of tissue on the display, which on whole helps increase the quality of diagnostics. However, in the context of problems to be resolved in oncology, the efficiency of currently available commercial tomography methods remains relatively low. One of the reasons is the lack of methods that would allow reliable differentiation between malignant and benign tumors on reconstructed tomograms. The recent clinical studies (Boas et al., 2001; Gibson et al., 2005) show that rapidly developing diffuse optical tomography (DOT) is very likely to help out. DOT is unique in its ability to separately reconstruct the spatial distributions of optical parameters (absorption and scattering coefficients) which helps visualize the spatial pattern of blood volume and oxygen saturation. As a result, it becomes possible to differentiate and spatially localize such phenomena as cancerous tissue vascularisation and angiogenesis and hence detect cancer in the early stage of its development. DOT implies that tissue is probed by near-infrared radiation from the so-called therapeutic window (700-900 nm) where absorption by tissue is minimal. Position dependent measurements are taken, i.e. near-infrared light from an array of sources is observed with an array of receivers. Then an inverse problem, i.e. the tomographic reconstruction problem is solved to infer the spatially localized optical properties of tissue. The main problem of DOT is the low spatial resolution because of the multiple scattering of photons that do not have regular trajectories and are distributed in the entire volume V being probed. As a result, each volume element significantly contributes to the detected signal. The basic equation of DOT is written as

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

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.

Optical diffuse tomography: fast trajectory algorithm of reconstruction

The paper is devoted to the problems of design of reconstruction algorithms for optical diffuse 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. Several analogies of curvilinear PAT in strongly scattering media with the usual optics rays are presented. It is shown that the PAT method is convenient for the time-domain optical diffuse tomography as well as for the frequency-domain one. The use of the trajectory approach opens promising opportunities for the increasing of the spatial resolution using methods designed in the convenient optics.