Diffuse Optical Tomography (DOT) involves a nonlinear optimization problem to find the tissue optical properties by measuring near-infrared light noninvasively. Many researchers used linearization methods to obtain the optical image in real time. However, the linearization procedure may neglect small but sometimes important regions such as small tumors at an early stage. Therefore, nonlinear optimization methods such as gradient- or Newton- type methods are
exploited, resulting in better resolution image than that of linearization methods. But the disadvantage of nonlinear
methods is that they need much computation time. To solve this trade-off dilemma between image resolution and computing time, we suggest second order inverse Born expansion algorithm in this paper. It is known that a small perturbation of photon density is represented by Born expansion with respect to the perturbation of optical coefficients, which is an infinite series of integral operators having Robin function kernel. Whereas, inverse Born expansion is an
implicit representation of a small perturbation of optical coefficients by an infinite series of the integral operators with
respect to the photon density and its perturbation, which is appropriate series expansion for inverse DOT problem.
Solving the inverse Born expansion itself and the first order approximation correspond to nonlinear and linear method,
respectively. We formulated a second order approximation of the inverse Born expansion explicitly to make numerical
implementation possible and showed the convergence order of the proposed method is higher than the linear method.
This work investigates the design of optimum distribution of photon density power among the source positions, and optimum modulation frequencies to maximize the detectability of heterogeneities embedded in turbid medium using near infrared light. The optimum waveforms are designed for the sources in near-infrared diffuse optical tomography which involves reconstruction of spatially varying optical properties of turbid medium as well as fluorophore lifetime and yield from boundary measurements. We start our analysis by first deriving the discrete source-to-detector map based on the finite-element formulation of the diffuse photon density wave equation and Robin boundary conditions. We determine statistical figures of merit to maximize the contrast of heterogeneities with respect to a given background. Next, we design optical waveforms that will maximize the figure of merit for the detectability of heterogeneities. When the figure of merit is derived based on optimal linear detection under the assumption of Gaussianity, the optimal source vector is given by the eigenvector corresponding to the maximum eigenvalue of the norm of the differences between the source-to-detector maps of homogeneous and heterogeneous domains. We extended our approach to investigate the optimum spatial positions and intensities of point sources to maximize the detectability of the heterogeneities. We explored the effect of tumor location with respect to the sources, tumor size, and the number of sources on detectability.
Diffuse optical tomography (DOT) in the near infrared involves reconstruction of spatially varying optical properties of turbid medium from boundary measurements based on a forward model of photon
propagation. Due to highly non-linear nature of the DOT, high quality image reconstruction is a computationally demanding problem that requires repeated solutions of both the forward and the inverse problems. Therefore, it is highly desirable to develop methods and algorithms that are computationally efficient. In this paper, we propose a domain decomposition approach to address the computational complexity of the DOT problem. We propose a two-level multiplicative overlapping domain decomposition method for the forward problem and a two-level space decomposition method for the inverse problem. We showed the convergence of the inverse solver and derived the computational complexity of each method. We demonstrate the performance of the proposed approach in numerical simulations.
Diffuse optical tomography is modelled as an optimization problem to find the absorption and scattering coefficients that minimize the error between the measured photon density function and the approximated one computed using the coefficients. The problem is composed of two steps: the forward solver to compute the photon density function and its Jacobian (with respect to the coefficients), and the inverse solver to update the coefficients based on the photon density function and its Jacobian attained in the forward solver. The resulting problem is nonlinear and highly ill-posed. Thus, it requires large amount of computation for high quality image. As such, for real time application, it is highly desirable to reduce the amount of computation needed. In this paper, domain decomposition method is adopted to decrease the computation complexity of the problem. Two level multiplicative overlapping domain decomposition method is used to compute the photon density function and its Jacobian at the inner loop and extended to compute the estimated changes in the coefficients in the outer loop. Local convergence for the two-level space decomposition for the outer loop is shown for the case when the variance of the coefficients is small.