Sparse-View X-Ray CT Reconstruction Using 𝓵1 Prior with Learned Transform

A major challenge in X-ray computed tomography (CT) is reducing radiation dose while maintaining high quality of reconstructed images. To reduce the radiation dose, one can reduce the number of projection views (sparse-view CT); however, it becomes difficult to achieve high quality image reconstruction as the number of projection views decreases. Researchers have applied the concept of learning sparse representations from (highquality) CT image dataset to the sparse-view CT reconstruction. We propose a new statistical CT reconstruction model that combines penalized weighted-least squares (PWLS) and `1 regularization with learned sparsifying transform (PWLS-ST-`1), and an algorithm for PWLS-ST-`1. Numerical experiments for sparse-view 2D fan-beam CT and 3D axial cone-beam CT show that the `1 regularizer significantly improves the sharpness of edges of reconstructed images compared to the CT reconstruction methods using edge-preserving regularizer and `2 regularization with learned ST.