  A major challenge in computed tomography (CT) is to reduce X-ray dose to a
low or even ultra-low level while maintaining the high quality of reconstructed
images. We propose a new method for CT reconstruction that combines penalized
weighted-least squares reconstruction (PWLS) with regularization based on a
sparsifying transform (PWLS-ST) learned from a dataset of numerous CT images.
We adopt an alternating algorithm to optimize the PWLS-ST cost function that
alternates between a CT image update step and a sparse coding step. We adopt a
relaxed linearized augmented Lagrangian method with ordered-subsets (relaxed
OS-LALM) to accelerate the CT image update step by reducing the number of
forward and backward projections. Numerical experiments on the XCAT phantom
show that for low dose levels, the proposed PWLS-ST method dramatically
improves the quality of reconstructed images compared to PWLS reconstruction
with a nonadaptive edge-preserving regularizer (PWLS-EP).
