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.
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