Linearization and reconstruction of nonlinear diffuse optical tomographic image

Abstract

Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f (x) = x T Ax − b T x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and illconditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f (The self guided spatial weighted prior (e T Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.

Differential photon waves imaging

“…Photons are thought and modeled as particles in Monte Carlo (MC) simulations 33‐54 or waves as in diffusion equation (DE) approximation which descent from nuclear radiative transfer equation (RTE) 55‐86 . Physical modeling of light transport inside the heterogeneous tissue is necessary for understanding and analyzing of weak energized photons in diffusive media.…”