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.

Nowadays, the Hough transform (HT) is a tool extensively used in image processing and computer vision. It finds applications ranging from line detection in images to tomographic reconstruction. Due to their numerous industrial applications, which comprise execution not only on remote servers but also on less powerful embedded devices and within the Internet of Things (IoT) paradigm, fast algorithms for computing the HT (fast HT, or FHT) that efficiently utilize computational memory are in high demand. In-place algorithms, which use memory allocated for the input data array and may employ a small amount of additional memory for intermediate calculations, are recognized to have such characteristics. For images with widths that are powers of two, such an algorithm is known; it is the in-place version of the de facto standard Brady–Yong algorithm. However, in practice, it is often needed to compute the FHT for images with arbitrary widths, to which the Brady–Yong algorithm is not applicable. In this paper, we propose an in-place \(\mathit{FHT}2\mathit{IDS}\) algorithm. It is a modification of the \(\mathit{FHT}2\mathit{DS}\) out-of-place algorithm for computing the FHT for images of arbitrary width previously presented in the literature. We justify correctness of the \(\mathit{FHT}2\mathit{IDS}\) algorithm and show that the result of processing an image of an arbitrary width matches the output of the \(\mathit{FHT}2\mathit{DS}\) algorithm. We demonstrate that the \(\mathit{FHT}2\mathit{IDS}\) algorithm allocates a significantly smaller data array at each recursion step compared to the \(\mathit{FHT}2\mathit{DS}\) algorithm: at each recursion step, it requires an array of size no greater than \(w+h\), rather than \(wh\), assuming that the input image has a \(w\times h\) shape. We also develop a nonrecursive version of the \(\mathit{FHT}2\mathit{IDS}\) algorithm, which is called the \(\mathit{FHT}2\mathit{IDS}\)-\(\mathit{NonRecursive}\) algorithm. The auxiliary space complexity of the \(\mathit{FHT}2\mathit{IDS}\)-\(\mathit{NonRecursive}\) algorithm is proved to be \(\mathcal{O}(w+h)\), while the \(\mathit{FHT}2\mathit{DS}\)-\(\mathit{NonRecursive}\) algorithm, a nonrecursive version of the \(\mathit{FHT}2\mathit{DS}\) algorithm, demonstrates the auxiliary space complexity of \(\mathcal{O}(wh)\), where \(w\) and \(h\) denote the dimensions of the input image. Experimental results show that the \(\mathit{FHT}2\mathit{IDS}\)-\(\mathit{NonRecursive}\) algorithm implemented in C/C\(\texttt{++}\) is 45% faster than its out-of-place counterpart, \(\mathit{FHT}2\mathit{DS}\)-\(\mathit{NonRecursive}\). The \(\mathit{FHT}2\mathit{IDS}\) and \(\mathit{FHT}2\mathit{IDS}\)-\(\mathit{NonRecursive}\) algorithms are also implemented in Python within an open-access adrt library, which the readers may find useful in their research.

The Hough (discrete Radon) transform (HT/DRT) is a digital image processing tool that has become indispensable in many application areas, ranging from general image processing to neural networks and X-ray computed tomography. The utilization of the HT in applied problems demands its computational efficiency and increased accuracy. The de facto standard algorithm for the fast HT is the Brady-Yong algorithm. However, it is applicable only to images of a power-of-two width. The algorithm that generalizes the Brady-Yong algorithm for non-power-of-two image width with the same asymptotic complexity is known, but it has not been studied neither in terms of the constant in the asymptotics nor in accuracy. Thus, supported both by theory and experiments, generalization of the Brady-Yong algorithm for images of arbitrary size while maintaining asymptotic computational complexity and acceptable accuracy remains of paramount necessity. In this paper, we proposed 5 novel algorithms that incorporate the core idea of the Brady-Yong algorithm and are suitable for computing the fast HT for images of arbitrary size. We investigated the properties of 5 new algorithms, along with one previously proposed algorithm from the literature, through both theoretical analysis and experimental validation. As one of our major contributions, among the proposed algorithms, we singled out a FHT2DT algorithm and proved that it provides a substantial compromise between accuracy and computational complexity. The FHT2DT algorithm is significantly more accurate than the algorithm previously suggested in the literature and, hence, FHT2DT can substitute it in practical applications. During the analysis of the properties of the proposed algorithms, we created a map that characterizes the algorithms based on their accuracy and speed parameters. Users can select the method that best suits their needs —- whether prioritizing computational complexity or accuracy —- by referring to our map.

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.

The Hough transform (HT) is a cornerstone technique applied in fields ranging from classical image processing to cutting-edge neural networks. Its algorithmic implementations are primarily evaluated along two directions: computational complexity and accuracy, where the latter is typically defined as the error of approximation of continuous lines by discrete ones implicitly constructed during the HT algorithm execution. Fast HT (FHT) algorithms with optimal linearithmic complexity are well established—for instance, the Brady–Yong algorithm for images with power-of-two sizes. Extensions such as FHT2DT generalize this efficiency to images of arbitrary shape, but at the expense of accuracy, which deteriorates with increasing image size. On the other hand, HT algorithms that maintain a bounded approximation error achieve higher accuracy but approach near-cubic complexity, making them impractical for large inputs. In this work, we introduce the FHT2SP algorithm, which combines near-optimal speed with high accuracy. Within the FHT2SP algorithm formulation, we extend Brady’s original superpixel definition—applicable solely to square images with power-of-two side lengths—so that it becomes applicable to rectangular images of arbitrary dimensions. Unlike Brady’s definition, which restricted superpixels to square shapes with power-of-two linear size, our superpixel definition permits them to take any rectangular form. The FHT2SP algorithm further incorporates our extended superpixel definition into the \(FHT2DT\) algorithm. By carefully selecting the superpixel size, the FHT2SP achieves nearly optimal linear-log-cubed complexity \(\Theta(wh\log^3 w)\) for an image of shape \(w\times h\), while guaranteeing a constant approximation error bound \(\lambda+1/2\) independent of image size, tunable via the FHT2SP meta-parameter \(\lambda\in(0,1]\). The auxiliary space complexity is shown to be \(\Theta(wh\log^2 w)\). We provide a summary table of experimental results, which can serve as practical guidance for selecting the value of the meta-parameter \(\lambda\) to balance accuracy, computational cost, and memory usage.