VVBP-Tensor in the FBP Algorithm: Its Properties and Application in Low-Dose CT Reconstruction

For decades, commercial X-ray computed tomography (CT) scanners have been using the filtered backprojection (FBP) algorithm for image reconstruction. However, the desire for lower radiation doses has pushed the FBP algorithm to its limit. Previous studies have made significant efforts to improve the results of FBP through preprocessing the sinogram, modifying the ramp filter, or postprocessing the reconstructed images. In this paper, we focus on analyzing and processing the stacked view-by-view backprojections (named VVBP-Tensor) in the FBP algorithm. A key challenge for our analysis lies in the radial structures in each backprojection slice. To overcome this difficulty, a sorting operation was introduced to the VVBP-Tensor in its ${z}$ direction (the direction of the projection views). The results show that, after sorting, the tensor contains structures that are similar to those of the object, and structures in different slices of the tensor are correlated. We then analyzed the properties of the VVBP-Tensor, including structural self-similarity, tensor sparsity, and noise statistics. Considering these properties, we have developed an algorithm using the tensor singular value decomposition (named VVBP-tSVD) to denoise the VVBP-Tensor for low-mAs CT imaging. Experiments were conducted using a physical phantom and clinical patient data with different mAs levels. The results demonstrate that the VVBP-tSVD is superior to all competing methods under different reconstruction schemes, including sinogram preprocessing, image postprocessing, and iterative reconstruction. We conclude that the VVBP-Tensor is a suitable processing target for improving the quality of FBP reconstruction, and the proposed VVBP-tSVD is an effective algorithm for noise reduction in low-mAs CT imaging. This preliminary work might provide a heuristic perspective for reviewing and rethinking the FBP algorithm.