Model based iterative reconstruction algorithms are capable of reconstructing high-quality images from lowdose CT measurements. The performance of these algorithms is dependent on the ability of a signal model to characterize signals of interest. Recent work has shown the promise of signal models that are learned directly from data. We propose a new method for low-dose tomographic reconstruction by combining adaptive sparsifying transform regularization within a statistically weighted constrained optimization problem. The new formulation removes the need to tune a regularization parameter. We propose an algorithm to solve this optimization problem, based on the Alternating Direction Method of Multipliers and FISTA proximal gradient algorithm. Numerical experiments on the FORBILD head phantom illustrate the utility of the new formulation and show that adaptive sparsifying transform regularization outperforms competing dictionary learning methods at speeds rivaling total-variation regularization.