Title: Sparse-View X-Ray CT Reconstruction Using $\ell_1$ Prior with Learned Transform,
Abstract: 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 (high-quality) 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 $\ell_1$
regularization with learned sparsifying transform (PWLS-ST-$\ell_1$), and an
algorithm for PWLS-ST-$\ell_1$. Numerical experiments for sparse-view 2D
fan-beam CT and 3D axial cone-beam CT show that the $\ell_1$ regularizer
significantly improves the sharpness of edges of reconstructed images compared
to the CT reconstruction methods using edge-preserving regularizer and $\ell_2$
regularization with learned ST.