EFFICIENT VARIANCE-REDUCED METHOD AND APPARATUS FOR MODEL-BASED ITERATIVE CT IMAGE RECONSTRUCTION

A method and apparatus is provided to reconstruct a computed tomography image using iterative reconstruction combined with variance-reduced acceleration techniques. The acceleration techniques including: ordered subsets, separable quadratic surrogates, and Nesterov's acceleration. Ordered subset iteration is used, but instead of calculating a gradient of the objective function for only one subset per iteration, a full gradient of the total objective function is used. This decreases the variance and mitigates limit cycles. A correction term is calculated as the difference between the subset gradient and the full gradient, and this correction term is used when performing the update of the reconstructed image. The ordered subset can be combined with Nesterov's acceleration. To improve computational efficiency, the full gradient can be calculated once every T iterations, with negligible degradation to the convergence rate.