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.

Reproducibility is a cornerstone of scientific progress, yet in X-ray computed tomography (CT) reconstruction, it remains a critical and unresolved challenge. Current benchmarking practices in CT are hampered by the scarcity of openly available datasets, the incomplete or task-specific nature of existing resources, and the lack of transparent implementations of widely used methods and evaluation metrics. As a result, even the fundamental property of reproducibility is frequently violated, undermining objective comparison and slowing methodological progress. In this work, we analyze the systemic limitations of current CT benchmarking, drawing parallels with broader reproducibility issues across scientific domains. We propose an extended data model and formalized schemes for data preparation and quality assessment, designed to improve reproducibility and broaden the applicability of CT datasets across multiple tasks. Building on these schemes, we introduce checklists for dataset construction and quality assessment, offering a foundation for reliable and reproducible benchmarking pipelines. A key aspect of our recommendations is the integration of virtual CT (vCT), which provides highly realistic data and analytically computable phantoms, yet remains underutilized despite its potential to overcome many current barriers. Our work represents a first step toward a methodological framework for reproducible benchmarking in CT. This framework aims to enable transparent, rigorous, and comparable evaluation of reconstruction methods, ultimately supporting their reliable adoption in clinical and industrial applications.

Monitored tomographic reconstruction (MTR) is a potentially powerful tool for dose and time reduction in computed tomography scanning. We are the first to study the issue of practical implementation of MTR protocols in current-generation real-life instruments. We propose an empirical quantitative model for calculating acquisition and reconstruction times. It is demonstrated that projection acquisition order has a significant impact on the time and dose of tomographic experiments. The new alternative acquisition most suitable for MTR protocols is proposed. To estimate the restrictions and scope of applicability for MTR four typical commercial setups are studied within a proposed model. We construct an experimental stand for achieving a real-time reconstruction, together with validation of the proposed acquisition time model. We demonstrate that real-time reconstruction may be implemented without slowing down an acquisition process. An optimization of reconstruction from partial data is proposed, which allowed the production of 385 and 440 reconstructions for standard and proposed acquisition orders correspondingly during a single acquisition of 512 projections. The results of the study demonstrate that with proposed optimizations MTR can be effectively utilized for practical applications using the current generation of existing setups in industrial and nano tomography fields.

Orthotropic alignment of 3D images refers to setting a volume’s orientation according to its orthotropic properties. It is particularly important in industrial computed tomography (CT), where alignment enables standardized orientation of similar objects, facilitating registration, including CAD-model registration, for precise defect measurement. Orthotropic alignment is critical in applications such as printed circuit board (PCB) inspection and analysis of complex components, e.g., measuring engine blade clearances. In the latter case, slices must align with specific anisotropic axes, which may not fully correspond to orthotropic properties, representing another practical scenario. Existing orthotropic alignment methods, however, suffer from limited accuracy and applicability. In this paper, we formalize the task and propose a robust, efficient, reproducible, fully automatic approach for aligning various volumes. Our method leverages a 3D fast Hough transform (FHT) to compute sums across a set of planes, enabling reliable detection of anisotropic axes and orthotropic features. The FHT has been successfully applied in 2D image processing and document recognition; here, extended to three dimensions, it serves as an effective tool for orthotropic alignment. While a naive implementation would require O(N⁵) operations, the 3D FHT reduces this to O(N³ log N), making it comparable with classical tensor-based approaches. We provide the implementation, evaluation, and assessment of the algorithm on both real and synthetic CT data. The results outperform baseline methods in both quality and robustness, while offering broader applicability and fewer optimization parameters. Potential applications in related fields are also discussed.

The article presents the results of research in the field of computational X-ray tomography, obtained within the framework of the scientific school, by Doctor of Engineering, Corresponding Member of the Russian Academy of Sciences V.L. Arlazarov, on artificial intelligence. The field of computed tomography, which is relatively young for the school, arose as a result of a combination of combinatorial optimization approaches, training neural network models, image processing, and solving the problem of stopping information acquisition. Thanks to the accumulated experience, four areas of research can be distinguished: fast algorithms for tomographic reconstruction, scanning protocols for monitored tomographic reconstruction, neural network approaches to reconstruction, as well as methods for suppressing artifacts and distortions that occur in tomographic reconstructions. This article reflects the main successes and achievements obtained in these areas, which are demonstrated using the example of specific applied solutions.