A Splitting-based Iterative Algorithm for Accelerated Statistical X-ray CT Reconstruction
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Statistical image reconstruction using penalized weighted least-squares (PWLS) criteria can improve image-quality in X-ray computed tomography (CT). However, the huge dynamic range of the statistical weights leads to a highly shift-variant inverse problem making it difficult to precondition and accelerate existing iterative algorithms that attack the statistical model directly. We propose to alleviate the problem by using a variable-splitting scheme that separates the shift-variant and ("nearly") invariant components of the statistical data model and also decouples the regularization term. This leads to an equivalent constrained problem that we tackle using the classical method-of-multipliers framework with alternating minimization. The specific form of our splitting yields an alternating direction method of multipliers (ADMM) algorithm with an inner-step involving a "nearly" shift-invariant linear system that is suitable for FFT-based preconditioning using cone-type filters. The proposed method can efficiently handle a variety of convex regularization criteria including smooth edge-preserving regularizers and nonsmooth sparsity-promoting ones based on the l(1)-norm and total variation. Numerical experiments with synthetic and real in vivo human data illustrate that cone-filter preconditioners accelerate the proposed ADMM resulting in fast convergence of ADMM compared to conventional (nonlinear conjugate gradient, ordered subsets) and state-of-the-art (MFISTA, split-Bregman) algorithms that are applicable for CT.
Self-supervised learning for CT image denoising and reconstruction: a review.
Choi K Biomed Eng Lett. 2024; 14(6):1207-1220.
PMID: 39465103 PMC: 11502646. DOI: 10.1007/s13534-024-00424-w.
Chi J, Wei X, Sun Z, Yang Y, Yang B J Imaging Inform Med. 2024; 37(4):1902-1921.
PMID: 38378965 PMC: 11300784. DOI: 10.1007/s10278-024-00979-1.
Jin R, Li Y, Shosted R, Xing F, Gilbert I, Perry J Magn Reson Med. 2023; 91(1):61-74.
PMID: 37677043 PMC: 10847962. DOI: 10.1002/mrm.29812.
Jin R, Shosted R, Xing F, Gilbert I, Perry J, Woo J Magn Reson Med. 2022; 89(2):652-664.
PMID: 36289572 PMC: 9712260. DOI: 10.1002/mrm.29486.
Lee M, Yun C, Kim K, Lee Y Metabolites. 2022; 12(3).
PMID: 35323674 PMC: 8954205. DOI: 10.3390/metabo12030231.