We propose a Learned Primal-Dual algorithm for tomographic reconstruction. The algorithm includes the (possibly non-linear) forward operator in a deep neural network inspired by unrolled proximal primal-dual optimization methods, but where the proximal operators have been replaced with convolutional neural networks. The algorithm is trained end-to-end, working directly from raw measured data and does not depend on any initial reconstruction such as Filtered Back-Projection (FBP). We evaluate the algorithm on low dose Computed Tomography (CT) reconstruction using both analytic and human phantoms against classical reconstruction given by FBP and total variation (TV) regularized reconstruction as well as deep learning based post-processing of a FBP reconstruction. For the analytic data we demonstrate Peak Signal to Noise Ratio (PSNR) improvements of > 10 dB when compared to both TV reconstruction and learned post-processing. For the human phantom we demonstrate a 6.6 dB improvement compared to TV and a 2.2 dB improvement as compared to learned postprocessing. The proposed algorithm also improves upon the compared algorithms with respect to the structural similarity index (SSIM) and the evaluation time is ≈ 600 ms for a 512×512 pixel dataset.
In contrast, the learned primal-dual algorithm proposed by REF replaces the proximal operators in (1.2) by convolutional neural networks, and keeps the linear operator fixed.
Learned Primal-dual Reconstruction
IEEE Transactions on Medical Imaging (2018)
Computer Science Medicine Mathematics