The maximum-likelihood expectation-maximization (ML-EM) algorithm is used for an iterative image reconstruction (IIR) method and performs well with respect to the inverse problem as cross-entropy minimization in computed tomography. For accelerating the convergence rate of the ML-EM, the ordered-subsets expectation-maximization (OS-EM) with a power factor is effective. In this paper, we propose a continuous analog to the power-based accelerated OS-EM algorithm. The continuoustime image reconstruction (CIR) system is described by nonlinear differential equations with piecewise smooth vector fields by a cyclic switching process. A numerical discretization of the differential equation by using the geometric multiplicative first-order expansion of the nonlinear vector field leads to an exact equivalent iterative formula of the power-based OS-EM. The convergence of nonnegatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem for consistent inverse problems. We illustrate through numerical experiments that the convergence characteristics of the continuous system have the highest quality compared with that of discretization methods. We clarify how important the discretization method approximates the solution of the CIR to design a better IIR method.

We propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

It has been reported that a reduction in tube kilovoltage during computed tomography (CT) angiography results in an average reduction of the effective radiation dose. Furthermore, a lower kilovoltage has been shown as a technique dose. However, there is no fundamental data in a low-kilovoltage protocol for CT venography. Thus, the purpose of this study was to investigate contrast enhancement, image noise, and radiation exposure with lower kilovoltage on CT images scanned using phantom of lower limbs and clinical CT images. In order to grasp the effective energy in each tube voltage of the equipment used, we determined the half-value layer using aluminum attenuation coefficient. The phantom of the lower was sealed with contrast agent that was adjusted in various CT values. We scanned this phantom at 80 kVp, 100 kVp, and 120 kVp settings, and evaluated the changes in CT value. We also compared CT values, CTDIvol, contrast enhancement, and radiation exposure with 100 kVp and 120 kVp in patients with suspected pulmonary embolism or deep venous thrombosis. We found the CT value increased 30 HU with 100 kVp settings, and contrast was also improved. A reduction of radiation exposure without deterioration of image quality would be possible by lowering the kilovoltage setting in CT venography.

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