Learnable Douglas-Rachford iteration and its applications in DOT imaging

How to overcome the ill-posed nature of inverse problems is a pervasive problem in medical imaging. Most existing solutions are based on regularization techniques. This paper proposed a deep neural network (DNN) based image reconstruction method, the so-called DR-Net, that leverages the interpretability of existing regularization methods and adaptive modeling capacity of DNN. Motivated by a Douglas-Rachford fixed-point iteration for solving \begin{document}$ \ell_1 $\end{document} -norm relating regularization model, the proposed DR-Net learns the prior of the solution via a U-Net based network, as well as other important regularization parameters. The DR-Net is applied to solve image reconstruction problem in diffusion optical tomography (DOT), a non-invasive imaging technique with many applications in medical imaging. The experiments on both simulated and experimental data showed that the proposed DNN based image reconstruction method significantly outperforms existing regularization methods.