Accelerating ordered-subsets image reconstruction for x-ray CT using double surrogates

Abstract

Conventional ordered-subsets (OS) methods for regularized image reconstruction involve computing the gradient of the regularizer for every subset update. When dealing with large problems with many subsets, such as in 3D X-ray CT, computing the gradient for each subset update can be very computationally expensive. To mitigate this issue, some investigators use unregularized iterations followed by a denoising operation after updating all subsets.1 Although such methods save computation, their convergence properties are uncertain, and since they may not be minimizing any particular cost function it becomes more difficult to design regularization parameters. Furthermore, it is known that inserting filtering steps into unregularized algorithms can lead to undesirable spatial resolution properties.2 Our goal here is to reduce the computational cost without inducing such problems. We propose a new OS-type algorithm that is derived using optimization transfer principles. The proposed method allows the gradient of the regularizer to be updated less frequently, and thus reduces the computational expense when many subsets are used. Our derivation leads to a correction term that accounts for the fact that the regularizer gradient is updated less frequent than every sub-iteration. Simulations and a phantom experiment show that the proposed method reconstructed images with compatible image quality within reduced computation time.