Wang Linyuan, Zhang Hanming, Cai Ailong, Li Yongl, Yan Bin, Li Lei, Hu Guoen
National Digital Switching System Engineering and Technological Research Center, Zhengzhou, Henan, China.
He Nan Province People's Hospital, Zhengzhou, Henan, China.
J Xray Sci Technol. 2015;23(1):1-10. doi: 10.3233/XST-140465.
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.
采用诸如总变差（TV）最小化等利用稀疏性方法的迭代图像重建（IIR），用于压缩感知（CS）研究，声称可能大幅减少采样要求。对计算机断层扫描（CT）而言，量化这一说法并非易事，因为欠采样重建的奇异性以及稀疏视图重建所需的足够视图数量都不明确。本文采用奇异值分解方法研究系统矩阵和正则化矩阵的条件数及奇异性。提出了一种经验下界估计方法，这有助于估计精确重建所需的投影视图数量。仿真研究表明，通过正则化可有效降低不同投影视图下系统矩阵的奇异性。计算正则化矩阵的条件数对于评估使用正则化的重建算法的奇异性和恢复潜力提供参考是必要的。经验下界有助于用稀疏重建算法估计投影视图数量。
