# Algorithms in Tomography and Related Inverse Problems--A Review
## 1 Introduction
### Tomographic Reconstruction Techniques, Principles, and New Approaches
(2018), the authors delve into the fundamental tenets of computed tomography, offering insights into the methodologies for acquiring computed tomography scans. These methods employ X-ray tubes and synchrotron sources, as well as various feasible contrast modes. Such a thorough understanding of the technology underpinning tomographic imaging is vital for researchers and clinicians alike. Understanding the impact of acquisition parameters on reconstruction quality is essential. The significance of post-processing techniques comes to the forefront in work by [PERSON] and [PERSON] (2018). As outlined by [PERSON], [PERSON] et al. (2018), the research introduces the concept of equally inclined tomography, an advanced method for reconstructing three-dimensional objects from multiple two-dimensional projections. This innovative approach supersedes traditional tomography, which relies on equally angled two-dimensional projections. The result is a significant enhancement in three-dimensional reconstruction quality. Meanwhile, [PERSON], [PERSON] et al. (2018) take a pioneering step in the realm of neural network design for positron emission tomography. The direct PET neural network is proficient in reconstructing multi-domain image volumes from sinograms, underlining the growing role of artificial intelligence in the field. As reported by [PERSON], [PERSON] et al. (2018), the research sets the stage for a deep learning revolution in tomographic imaging. The primary objective of the study is to attain high-quality three-dimensional reconstructed images in the context of sparse sampling conditions. Deep learning methods promise to revolutionize accuracy and efficiency in the field. In a fusion of innovation and network architecture, [PERSON], [PERSON] et al. (2018) introduce a cascaded residual dense spatial-channel attention network. This network aims to reconstruct tomographic images from a limited number of projection views, amplifying the power of deep learning and data fidelity layers. For scenarios with limited data, [PERSON] and [PERSON] (2018) present a direct approach for limited-angle tomographic reconstruction, employing convolutional networks. The network training process involves minimizing the mean squared error between the network-generated reconstructions and a ground truth three-dimensional volume. This reference underscores the importance of employing software tools like Adobe Photoshop,ImageJ, Corel PHOTO-PAINT, and Origin to enhance the quality of images for quantitative analysis. Such post-processing techniques are instrumental in distinguishing between various diseases and disorders. These guide us from fundamental principles to cutting-edge innovations, all emphasizing the real-world impact in medical, industrial, and scientific applications. All these underscore the dynamic evolution of the field as it adapts to emerging technologies, harnesses the power of artificial intelligence, and continually strives for higher quality and efficiency. In this ever-advancing discipline, these references serve as beacons, illuminating the path for researchers and practitioners, ensuring that they remain at the forefront of tomographic imaging, and delivering high-quality solutions for an array of applications.