Fast, accurate and robust sparse-view CT reconstruction via residual-guided Golub-Kahan iterative reconstruction technique (RGIRT)

Reduction of projection views in X-ray computed tomography (CT) can protect patients from over exposure to ionizing radiation, thus is highly attractive for clinical applications. However, image reconstruction for sparse-view CT which aims to produce decent images from few projection views remains a challenge. To address this, we propose a Residual-guided Golub-Kahan Iterative Reconstruction Technique (RGIRT). RGIRT utilizes an inner-outer dual iteration framework, with a flexible least square QR (FLSQR) algorithm implemented in the inner iteration and a restarted iterative scheme applied in the outer iteration. The inner FLSQR employs a flexible Golub-Kahan (FGK) bidiagonalization method to reduce the dimension of the inverse problem, and a weighted generalized cross-validation (WGCV) method to adaptively estimate the regularization hyper-parameter. The inner iteration efficiently yields the intermediate reconstruction result, while the outer iteration minimizes the residual and refines the solution by using the result obtained from the inner iteration. Reconstruction performance of RGIRT is evaluated and compared to other reference methods (FBPConvNet, SART-TV, and FLSQR) using realistic mouse cardiac micro-CT data. Experiment results demonstrate RGIRT’s merits for sparse-view CT reconstruction in high accuracy, efficient computation, and stable convergence. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work was partially supported by National Natural Science Foundation of China under grants 12101406 (JJ), 62105205 (WR), 62273238 (GC), Shanghai Science and Technology Innovation Program under grant 21YF1429100 (JJ), and start-up funding of ShanghaiTech University (WR, GC). ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced in the present study are available upon reasonable request to the authors.