Addressing contemporary challenges in computed tomography (CT) demands precise and efficient reconstruction. This necessitates the optimization of CT methods, particularly by improving the algorithmic efficiency of the most computationally demanding operators—forward projection and backprojection. Every measurement setup requires a unique pair of these operators. While fast algorithms for calculating forward projection operators are adaptable across various setups, they fall short in three-dimensional scanning scenarios. Hence, fast algorithms are imperative for backprojection, an integral aspect of all established reconstruction methods. This paper introduces a general method for the calculation of backprojection operators in any measurement setup. It introduces a versatile method for transposing summation-based algorithms, which rely exclusively on addition operations. The proposed approach allows for the transformation of algorithms designed for forward projection calculation into those suitable for backprojection, with the latter maintaining asymptotic algorithmic complexity. Employing this method, fast algorithms for both forward projection and backprojection have been developed for the 2D few-view parallel-beam CT as well as for the 3D cone-beam CT. The theoretically substantiated complexity values for the proposed algorithms align with their experimentally derived estimates.

Standard approaches to tomography reconstruction of the projection data registered with polychromatic emission lead to the appearance of cupping artifacts and irrelevant lines between regions of strong absorption. The main reason for their appearance is the fact that part of the emission with low energy is being absorbed entirely by high absorbing objects. This fact is known as beam hardening (BH). The procedure of processing projection data collected in polychromatic mode is presented; it reduces artifacts relevant to BH and does not require additional calibration experiments. The procedure consists of two steps: the first is to linearize the projection data with one‐parameter power correction, and the second is to reconstruct the images from linearized data. Automatic parameter adjustment is the main advantage of the procedure. The optimization problem is formulated. The system flowchart is presented. The reconstruction with different powers of correction is considered to evaluate the quality reconstruction.

Detailed and accurate three-dimensional (3D) information about the morphology of hierarchically structured materials is derived from multi-scale X-ray computed tomography (XCT) and subsequent 3D data reconstruction. High-resolution X-ray microscopy and nano-XCT are suitable techniques to nondestructively study nanomaterials, including porous or skeleton materials. However, laboratory nano-XCT studies are very time-consuming. To reduce the time-to-data by more than an order of magnitude, we propose taking advantage of a monitored tomographic reconstruction. The benefit of this new protocol for 3D imaging is that the data acquisition for each projection is interspersed by image reconstruction. We demonstrate this new approach for nano-XCT data of a novel transition-metal-based materials system: MoNi₄ electrocatalysts anchored on MoO₂ cuboids aligned on Ni foam (MoNi₄/MoO₂@Ni). Quantitative data that describe the 3D morphology of this hierarchically structured system with an advanced electrocatalytically active nanomaterial are needed to tailor performance and durability of the electrocatalyst system. We present the framework for monitored tomographic reconstruction, construct three stopping rules for various reconstruction quality metrics and provide their experimental evaluation.

Ring artifacts pose a major barrier to obtaining precise reconstruction in computed tomography (CT). The presence of ring artifacts complicates the use of automatic means of processing CT reconstruction results, such as segmentation, correction of geometric shapes, alignment of reconstructed volumes. Although there are numerous efficient methods for suppressing ring artifacts, many of them appear to be manual. Along with this, a large proportion of the automatic methods cope unsatisfactorily with the target task while requiring computational capacity. The current work introduces a projection data preprocessing method for suppressing ring artifacts that constitutes a compromise among the outlined aspects – automaticity, high efficiency and computational speed. Derived as the automation of the classical sinogram normalization method, the proposed method specific advantages consist in adaptability in relation to the filtered sinograms and the edge-preservation property proven within the experiments on both synthetic and real CT data. Concerning the challenging open-access data, the method has performed superior quality comparable to that of the advanced methods: it has demonstrated 70.4% ring artifacts suppression percentage (RASP) quality metric. In application to our real laboratory CT data, the proposed method allowed us to gain significant refinement of the reconstruction quality which has not been surpassed by a range of compared manual ring artifacts suppression methods.

In computed tomography, state-of-the-art reconstruction is based on neural network (NN) algorithms. However, NN reconstruction algorithms can be not robust to small noise-like perturbations in the input signal. A not robust NN algorithm can produce inaccurate reconstruction with plausible artifacts that cannot be detected. Hence, the robustness of NN algorithms should be investigated and evaluated. There have been several attempts to construct the numerical metrics of the NN reconstruction algorithms’ robustness. However, these metrics estimate only the probability of the easily distinguishable artifacts occurring in the reconstruction. However, these methods measure only the probability of appearance of easily distinguishable artifacts on the reconstruction, which cannot lead to misdiagnosis in clinical applications. In this work, we propose a new method for numerical estimation of the robustness of the NN reconstruction algorithms. This method is based on the probability evaluation for NN to form such selected additional structures during reconstruction which may lead to an incorrect diagnosis. The method outputs a numerical score value from 0 to 1 that can be used when benchmarking the robustness of different reconstruction algorithms. We employed the proposed method to perform a comparative study of seven reconstruction algorithms, including five NN-based and two classical. The ResUNet network had the best robustness score (0.65) among the investigated NN algorithms, but its robustness score is still lower than that of the classical algorithm SIRT (0.989). The investigated NN models demonstrated a wide range of robustness scores (0.38–0.65). Thus, in this work, robustness of 7 reconstruction algorithms was measured using the new proposed score and it was shown that some of the neural algorithms are not robust.