Iterative Tomographic Image Reconstruction Algorithm Based on Extended Power Divergence by Dynamic Parameter Tuning.

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.

Structure-changeable luminescent Eu(III) complex as a human cancer grade probing system for brain tumor diagnosis.

Accurate determination of human tumor malignancy is important for choosing efficient and safe therapies. Bioimaging technologies based on luminescent molecules are widely used to localize and distinguish active tumor cells. Here, we report a human cancer grade probing system (GPS) using a water-soluble and structure-changeable Eu(III) complex for the continuous detection of early human brain tumors of different malignancy grades. Time-dependent emission spectra of the Eu(III) complexes in various types of tumor cells were recorded. The radiative rate constants (kr), which depend on the geometry of the Eu(III) complex, were calculated from the emission spectra. The tendency of the kr values to vary depended on the tumor cells at different malignancy grades. Between T = 0 and T = 3 h of invasion, the kr values exhibited an increase of 4% in NHA/TS (benign grade II gliomas), 7% in NHA/TSR (malignant grade III gliomas), and 27% in NHA/TSRA (malignant grade IV gliomas). Tumor cells with high-grade malignancy exhibited a rapid upward trend in kr values. The cancer GPS employs Eu(III) emissions to provide a new diagnostic method for determining human brain tumor malignancy.

Block-Iterative Reconstruction from Dynamically Selected Sparse Projection Views Using Extended Power-Divergence Measure.

Iterative reconstruction of density pixel images from measured projections in computed tomography has attracted considerable attention. The ordered-subsets algorithm is an acceleration scheme that uses subsets of projections in a previously decided order. Several methods have been proposed to improve the convergence rate by permuting the order of the projections. However, they do not incorporate object information, such as shape, into the selection process. We propose a block-iterative reconstruction from sparse projection views with the dynamic selection of subsets based on an estimating function constructed by an extended power-divergence measure for decreasing the objective function as much as possible. We give a unified proposition for the inequality related to the difference between objective functions caused by one iteration as the theoretical basis of the proposed optimization strategy. Through the theory and numerical experiments, we show that nonuniform and sparse use of projection views leads to a reconstruction of higher-quality images and that an ordered subset is not the most effective for block-iterative reconstruction. The two-parameter class of extended power-divergence measures is the key to estimating an effective decrease in the objective function and plays a significant role in constructing a robust algorithm against noise.

Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures.

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.