title: System matrix analysis for sparse-view iterative image reconstruction in X-ray CT.
abstract: Iterative image reconstruction (IIR) with sparsity-exploiting methods, such as total variation (TV) minimization, used for investigations in compressive sensing (CS) claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is non-trivial, as both the singularity of undersampled reconstruction and the sufficient view number for sparse-view reconstruction are ill-defined. In this paper, the singular value decomposition method is used to study the condition number and singularity of the system matrix and the regularized matrix. An estimation method of the empirical lower bound is proposed, which is helpful for estimating the number of projection views required for exact reconstruction. Simulation studies show that the singularity of the system matrices for different projection views is effectively reduced by regularization. Computing the condition number of a regularized matrix is necessary to provide a reference for evaluating the singularity and recovery potential of reconstruction algorithms using regularization. The empirical lower bound is helpful for estimating the projections view number with a sparse reconstruction algorithm.
authors.affiliation: National Digital Switching System Engineering and Technological Research Center, Zhengzhou, Henan, China.
authors.forename: Linyuan
authors.initials: L
authors.lastname: Wang
authors.affiliation: National Digital Switching System Engineering and Technological Research Center, Zhengzhou, Henan, China.
authors.forename: Hanming
authors.initials: H
authors.lastname: Zhang
authors.affiliation: National Digital Switching System Engineering and Technological Research Center, Zhengzhou, Henan, China.
authors.forename: Ailong
authors.initials: A
authors.lastname: Cai
authors.affiliation: He Nan Province People's Hospital, Zhengzhou, Henan, China.
authors.forename: Yongl
authors.initials: Y
authors.lastname: Li
authors.affiliation: National Digital Switching System Engineering and Technological Research Center, Zhengzhou, Henan, China.
authors.forename: Bin
authors.initials: B
authors.lastname: Yan
authors.affiliation: National Digital Switching System Engineering and Technological Research Center, Zhengzhou, Henan, China.
authors.forename: Lei
authors.initials: L
authors.lastname: Li
authors.affiliation: National Digital Switching System Engineering and Technological Research Center, Zhengzhou, Henan, China.
authors.forename: Guoen
authors.initials: G
authors.lastname: Hu
mesh_terms: D000465:Algorithms; D008954:Models, Biological; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000379:methods*
keywords: System matrix analysis; condition number; projection views number; singularity; sparse-view reconstruction; total variation regularization