Mixed Total Variation and L¹ Regularization Method for Optical Tomography Based on Radiative Transfer Equation

Area of Science:

• Biomedical optics
• Molecular imaging
• Medical physics

Background:

• Optical tomography is an emerging imaging modality for reconstructing human tissue optical properties.
• Accurate reconstruction of optical properties, like absorption coefficient, is crucial for molecular imaging.
• Ill-posed inverse problems in optical tomography often require regularization techniques.

Purpose of the Study:

• To develop and validate a novel optical tomography method for reconstructing the absorption coefficient based on the radiative transfer equation (RTE).
• To enhance reconstruction accuracy for piecewise constant and sparse coefficient distributions by combining Total Variation (TV) and L1 regularization norms.

Main Methods:

• Discretization of the forward problem using the discontinuous Galerkin method (spatial) and finite element method (angular).
• Solving the minimization problem with a Jacobian-based Levenberg-Marquardt type method incorporating split Bregman algorithms for L1 regularization.
• Utilizing the adjoint method for efficient computation of the Jacobian matrix.

Main Results:

• The proposed method effectively reconstructs absorption coefficients from optical tomography data.
• Simulation results demonstrate the validity and efficiency of the combined TV and L1 regularization approach.
• The adjoint method significantly improves computational efficiency compared to other reconstruction methods.

Conclusions:

• The combined TV and L1 regularization offers superior reconstruction of piecewise constant and sparse optical properties in tissues.
• The developed optical tomography method is efficient and accurate for molecular imaging applications.
• This approach advances the field of optical tomography for biomedical applications.