Fully Nonlinear ${SP}_{3}$ Approximation Based Fluorescence Optical Tomography.

Area of Science:

• Biomedical Optics
• Medical Imaging
• Computational Science

Background:

• Current fluorescence optical tomography research often focuses on linear or linearized reconstruction problems.
• The nonlinear reconstruction problem offers more accurate modeling for improved imaging.
• Efficient forward models are crucial for accurate tomographic reconstructions.

Purpose of the Study:

• To develop and demonstrate a Gauss-Newton-based fully nonlinear reconstruction method for fluorescence optical tomography.
• To implement and compare nonlinear and linearized reconstruction schemes.
• To investigate shape reconstruction using radial-basis-function represented level-set-based methods.

Main Methods:

• Utilized an approximation to the radiative transfer equation (RTE) for forward modeling.
• Employed Gauss-Newton optimization for fully nonlinear reconstruction.
• Calculated Frechet derivatives for the nonlinear problem.
• Implemented finite-element method (FEM) and radial-basis-function (RBF) level-set methods for representation.

Main Results:

• Successfully demonstrated nonlinear reconstructions for tumor-mimicking objects in scattering and absorption-dominant settings.
• Showcased Frechet derivative calculations for the approximated RTE.
• Presented comparisons highlighting the benefits of nonlinear over linearized schemes, particularly in absorption-dominant media.
• Validated the formulation with moderately noisy data.

Conclusions:

• The proposed nonlinear reconstruction method is viable for fluorescence optical tomography.
• Nonlinear reconstruction offers significant advantages over linearized approaches, especially for absorption-dominant scenarios.
• The use of approximated RTE and advanced shape representations enhances reconstruction accuracy and efficiency.