# Algorithms in Tomography and Related Inverse Problems--A Review
## 1 Introduction
### Tomographic Reconstruction Techniques, Principles, and New Approaches
[9] introduce a swift and precise approach to tackle circular artifacts that often stem from missing segments of the Discrete Fourier Theorem. This method refines the precision and efficiency of image reconstruction, contributing to the overall quality of results. This approach is rooted in the precise partitioning of the Discrete Fourier Theorem space under the projective Discrete Radon Transform, as denoted in the Discrete Fourier Theorem. To further augment image quality and move beyond the confines of conventional backprojection methods, [PERSON], [PERSON] et al. [10] precede two innovative backprojection variants: the \(\alpha\)-trimmed backprojection and the principal component analysis-based backprojection. These variants offer the promise of superior image quality, which is a critical factor in numerous tomographic applications. As we advance in our exploration, [PERSON] [11] adopts a comprehensive methodology by implementing both the Algebraic Reconstruction Technique and Filter Backprojection methods. The study then rigorously compares the ensuing experimental results using performance metrics across various test cases. Such comparisons are instrumental in assisting researchers in selecting the most suitable method for their specific scenarios. As we delve into the field of computed tomography, [PERSON], [PERSON] et al. [12] focus on the correlation between the thickness of acquired computed tomography slices and the accuracy of three-dimensional volume reconstruction. This correlation is pivotal for radiation therapy planning and disease diagnosis. On the theoretical front, [PERSON] and [PERSON] [13]explore the theoretical framework of emission-computed tomography. The article delves into novel numerical approaches based on regularization methods. Understanding the theoretical underpinnings of the image reconstruction process is instrumental in advancing the field. In a noteworthy departure from conventional approaches, [PERSON], [PERSON] al. (2018) point out a pioneering system concept and design for a computed tomography scanner. This innovative design, featuring two X-ray tubes and two detectors, holds the potential to surmount the limitations of traditional multi-detector row computed tomography. In the pursuit of innovation, [PERSON], [PERSON] et al. (2018) center on an innovative computed tomography acquisition method. This method enables simultaneous projection captures, potentially offering exceptionally rapid scans and reductions in radiation doses. This innovation exemplifies the ongoing efforts to optimize technology in the field. Continuing the pursuit of efficiency, [PERSON], [PERSON] et al. (2018) introduce a novel rapid backprojection operator for processing tomographic data. This algorithm offers a cost-effective solution and is compared against other swift transformation techniques using extensive real and simulated datasets. Peering into the future, as outlined by [PERSON] and [PERSON] (2018), forthcoming advances are anticipated in both hardware and software. Innovations like photon-counting computed tomography and the integration of artificial intelligence are poised to reshape the field. Returning to the practical realm, [PERSON], [PERSON] et al. (2018) emphasize the real-world impact of tomographic reconstruction, particularly in the realm of medical imaging. This reference provides a broader context, shedding light on representative outcomes and the pressing concerns that demand attention in the field. Beyond algorithmic aspects, the technological side of tomographic imaging is illuminated by [PERSON] (2018). This article presents an assessment of the fundamental physical principles and technical facets of the computed tomography scanner. It encompasses noteworthy advancements in computed tomography technology, positioning the field at the forefront of diagnostic and research applications. In the paper authored by [PERSON], [PERSON] et al.