# Algorithms in Tomography and Related Inverse Problems--A Review
## 1 Introduction
### Tomographic Implementation Algorithms  
In this subsection, we focus on the topics of image quality improvement and artifact reduction, elucidating techniques and strategies to increase the accuracy and fidelity of tomographic images. [PERSON] and [PERSON] [39] take us into the realm of tomosynthesis reconstruction algorithms. The discussion of residual blur minimization expands the dialogue that was initiated, emphasizing the practical challenge of improving image quality and accuracy, especially in 3D reconstruction. [PERSON], [PERSON] et al. [40] further investigate the challenge of region-of-interest computed tomography in the presence of measurement noise. They introduce a relaxation of data fidelity and consistency requirements, highlighting the complex nature of handling real-world imperfections in imaging processes. [PERSON], [PERSON] et al. [41] lead us to improve image quality and reduce artifacts through the deep learning process in breast tomosynthesis, illustrating the impact of state-of-the-art technology. This is in line with the theme of advancing tomographic reconstruction using modern computational techniques. Additionally, [PERSON], [PERSON] et al. [42] add deep learning to the discussion for mitigating sparse-view and limited-angle artifacts in digital breast tomosynthesis, highlighting the role of artificial intelligence in improving tomographic image quality. The pioneering approach presented by [PERSON], [PERSON] et al. [43] concerning metal artifact reduction emphasizes the critical practical aspect of image artifact reduction, further linking to the general issue of image quality improvement. Referring to the optimization process, [PERSON], [PERSON], and [PERSON] [44] investigate the effect of projection geometry on caries detection. This is crucial as it addresses the real issue of optimizing image acquisition for specific diagnostic purposes, highlighting the importance of tailored imaging strategies. The authors [PERSON], [PERSON] et al. [45] lead us into the field of optimizing X-ray CT trajectories. Customizing imaging paths for specific samples addresses the practical challenge of efficient data acquisition and high-quality image production, coordinating the need for precision in tomographic imaging. Moving on to more widespread and synchronous processes, [PERSON], [PERSON] et al. [46] bridge the gap between iterative methods and deep learning, highlighting the potential of convolutional neural networks in dealing with ill-posed inverse problems. The regression approach discussed by [PERSON], [PERSON] et al. [47] demonstrated the integration of deep learning techniques with 3D spatial mapping, contributing to the multidimensional understanding of tomographic images. Finally, [PERSON] and [PERSON] [48] incorporate the current trend of image preprocessing and hyperparameter tuning using convolutional neural networks. The use of floating-point GPUs for image reconstruction by [PERSON] and [PERSON] [49] links technology to efficiency, demonstrating the importance of hardware developments in the field of tomography just as [PERSON], [PERSON] et al. [50] shed light on software solutions to streamline image reconstruction, highlighting the need for user-friendly tools that simplify the often-complex rebuilding process. The focus is shifting toward a hybrid gradient descent approach for region-of-interest CT. This methodology bridges the theoretical concepts, as reported by [PERSON], [PERSON] et al. [51], with practical applications, aiming to improve the accuracy and efficiency of tomographic reconstruction in specific regions of interest. [PERSON], [PERSON], and [PERSON] [52] introduce innovative methodologies for linear inverse problems in tomography. These methods resonate with the need to develop robust algorithms for accurate image reconstruction, a common thread among the discussed references.