Search

Computed tomography (CT) imaging plays a crucial role in various medical applications, but noise in projection data can significantly degrade image quality and hinder diagnosis accuracy. Iterative algorithms for tomographic image reconstruction outperform transform methods, especially in scenarios with severe noise in projections. In this paper, we propose a method to dynamically adjust two parameters included in the iterative rules during the reconstruction process. The algorithm, named the parameter-extended expectation-maximization based on power divergence (PXEM), aims to minimize the weighted extended power divergence between the measured and forward projections at each iteration. Our numerical and physical experiments showed that PXEM surpassed conventional methods such as maximum-likelihood expectation-maximization (MLEM), particularly in noisy scenarios. PXEM combines the noise suppression capabilities of power divergence-based expectation-maximization with static parameters at every iteration and the edge preservation properties of MLEM. The experimental results demonstrated significant improvements in image quality in metrics such as the structural similarity index measure and peak signal-to-noise ratio. PXEM improves CT image reconstruction quality under high noise conditions through enhanced optimization techniques. [ABSTRACT FROM AUTHOR]

Iterative reconstruction (IR) algorithms based on the principle of optimization are known for producing better reconstructed images in computed tomography. In this paper, we present an IR algorithm based on minimizing a symmetrized Kullback-Leibler divergence (SKLD) that is called Jeffreys’ J-divergence. The SKLD with iterative steps is guaranteed to decrease in convergence monotonically using a continuous dynamical method for consistent inverse problems. Specifically, we construct an autonomous differential equation for which the proposed iterative formula gives a first-order numerical discretization and demonstrate the stability of a desired solution using Lyapunov’s theorem. We describe a hybrid Euler method combined with additive and multiplicative calculus for constructing an effective and robust discretization method, thereby enabling us to obtain an approximate solution to the differential equation. We performed experiments and found that the IR algorithm derived from the hybrid discretization achieved high performance. [ABSTRACT FROM AUTHOR]

The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms provide significant improvements over transform methods in computed tomography. In this paper, we present an extended class of power-divergence measures (PDMs), which includes a large set of distance and relative entropy measures, and propose an iterative reconstruction algorithm based on the extended PDM (EPDM) as an objective function for the optimization strategy. For this purpose, we introduce a system of nonlinear differential equations whose Lyapunov function is equivalent to the EPDM. Then, we derive an iterative formula by multiplicative discretization of the continuous-time system. Since the parameterized EPDM family includes the Kullback–Leibler divergence, the resulting iterative algorithm is a natural extension of the maximum-likelihood expectation-maximization (MLEM) method. We conducted image reconstruction experiments using noisy projection data and found that the proposed algorithm outperformed MLEM and could reconstruct high-quality images that were robust to measured noise by properly selecting parameters. [ABSTRACT FROM AUTHOR]