Diffuse optical tomography through solving a system of quadratic equations: theory and simulations

Area of Science:

• Biomedical Optics
• Medical Imaging
• Computational Science

Background:

• Iterative image reconstruction is crucial for optical tomography.
• The established model-based iterative image reconstruction (MOBIIR) method uses a linear perturbation equation, limiting its ability to recover large contrast variations.

Purpose of the Study:

• To develop a novel iterative method for optical tomography using a nonlinear perturbation equation.
• To improve contrast recovery and noise tolerance in image reconstruction.

Main Methods:

• A nonlinear perturbation equation including second-derivative terms is employed for iterative updates of optical properties.
• The system of quadratic equations is solved using modified conjugate gradient descent or a two-step linearized predictor-corrector scheme.
• Derivatives are estimated using the adjoint of the forward operator.

Main Results:

• The nonlinear approach enables reconstructions with reasonable contrast recovery and accuracy without updating the perturbation equation in each iteration.
• Reintroducing an outer iteration with updated computed data improves performance.
• The method demonstrates recovery of large contrast variations in absorption coefficient with enhanced noise tolerance.

Conclusions:

• The proposed nonlinear iterative method significantly advances optical tomography reconstruction.
• It offers superior performance in recovering complex optical property variations compared to linear algorithms.
• This method holds promise for more accurate analysis of biological tissues in optical tomography applications.