RTE-based parameter reconstruction with TV+L1 regularization

Optical tomography is an imaging modality that explores the distribution of optical parameters in tissues. In this paper, the regularization jointing both TV and L1 norm is studied for absorption parameter identification based on radiative transport equation. The TV+L1 framework is introduced containing L2 data fidelity, TV regularizer and L1 regularizer. We demonstrate the existence, stability and convergence of the minima with respect to this TV+L1 regularization. A novel algorithm for solving related optimization problem is proposed based on reweighted method and technique of split-Bregman. Simulations are performed to show that the proposed reweighted TV+L1 regularization is more capable of preserving geometric structure of inclusions, quantifying values of absorption parameter and promoting fast convergence compared with TV or L1 regularization, and is potential for breast cancer imaging. Moreover, it is robust to noise.