Learning to Reconstruct CT Images from the VVBP-Tensor.

Deep learning (DL) is bringing a big movement in the field of computed tomography (CT) imaging. In general, DL for CT imaging can be applied by processing the projection or the image data with trained deep neural networks (DNNs), unrolling the iterative reconstruction as a DNN for training, or training a well-designed DNN to directly reconstruct the image from the projection. In all of these applications, the whole or part of the DNNs work in the projection or image domain alone or in combination. In this study, instead of focusing on the projection or image, we train DNNs to reconstruct CT images from the view-by-view backprojection tensor (VVBP-Tensor). The VVBP-Tensor is the 3D data before summation in backprojection. It contains structures of the scanned object after applying a sorting operation. Unlike the image or projection that provides compressed information due to the integration/summation step in forward or back projection, the VVBP-Tensor provides lossless information for processing, allowing the trained DNNs to preserve fine details of the image. We develop a learning strategy by inputting slices of the VVBP-Tensor as feature maps and outputting the image. Such strategy can be viewed as a generalization of the summation step in conventional filtered backprojection reconstruction. Numerous experiments reveal that the proposed VVBP-Tensor domain learning framework obtains significant improvement over the image, projection, and hybrid projection-image domain learning frameworks. We hope the VVBP-Tensor domain learning framework could inspire algorithm development for DL-based CT imaging.