Nonlinear inversion schemes for fluorescence optical tomography.

Area of Science:

• Biomedical Imaging
• Optical Tomography
• Medical Physics

Background:

• Fluorescence optical tomography (FOT) is a non-invasive imaging technique using fluorescent dyes to visualize biological structures.
• Accurate reconstruction of fluorophore distribution in FOT is challenging due to the nonlinear and ill-posed nature of light propagation in tissues.

Purpose of the Study:

• To investigate advanced Tikhonov regularization methods for improved FOT reconstruction.
• To compare nonlinear regularization techniques, including total-variation and level-set methods, against standard linear approaches.

Main Methods:

• Utilized a full three-dimensional nonlinear forward model based on partial differential equations.
• Employed Tikhonov regularization with nonlinear penalty terms (total-variation and level-set methods).
• Implemented Newton-type iterations for numerical realization and finite element methods for discretization.
• Applied adjoint methods for efficient implementation of sensitivity systems.

Main Results:

• Nonlinear regularization methods demonstrated superior reconstruction accuracy compared to linearized models and linear penalty terms.
• Numerical tests confirmed the effectiveness of total-variation and level-set regularization in FOT.
• Mesh-independent algorithms were achieved through careful discretization of continuous-level methods.

Conclusions:

• Nonlinear regularization techniques offer significant improvements for fluorescence optical tomography reconstruction.
• The proposed methods provide reliable and accurate imaging, overcoming limitations of conventional approaches.
• Careful numerical implementation ensures robust and mesh-independent reconstruction algorithms for FOT.