Adaptive Sparsifying Transforms for Iterative Tomographic Reconstruction

A major challenge in computed tomography imaging is to obtain high-quality images from low-dose measurements. Key to this goal are computationally efficient reconstruction algorithms combined with detailed signal models. We show that the recently introduced adaptive sparsifying transform (AST) signal model provides superior reconstructions from low-dose data at significantly lower cost than competing dictionary learning methods. We further accelerate this technique for tomography by utilizing the Linearized Alternating Direction Method of Multipliers (L-ADMM) to remove the need to solve an expensive least-squares problem that requires computing multiple forward and backward projections. Numerical experiments on data from clinical CT images show that adaptive sparsifying transform regularization outperforms total-variation and dictionary learning methods, and combining our regularizer with L-ADMM provides for faster reconstructions than standard ADMM.