# Algorithms in Tomography and Related Inverse Problems--A Review
## 1 Introduction
### Tomographic Imaging: From SAR, Geology, to Medical Advances  
In this comprehensive subsection, we are exploring advanced tomographic imaging techniques in various disciplines. The study presented by the authors [PERSON] and [PERSON] [58] leads us to the sphere of radar tomography (SAR), an innovative achievement that utilizes phase differences for the assessment of soil topography. It addresses a crucial issue, enhancing our ability to solve complex cases of stay-in SAR images, especially in multi-line imaging geometries. [PERSON] and [PERSON] [59] expand the understanding of SAR spacecraft, underlining its ability to distinguish the mechanisms of thoughts within pixels. This progress in SAR space tomography is aligned with the need for improved clarity and image accuracy. The acquisition of images based on the circular track, as analyzed by [PERSON] and [PERSON] [60], opens the capabilities of optimizing image processing at various azimile angles. This approach is particularly beneficial in studies such as building mining, highlighting the practical advantages of SAR data processing. As we deepen our searches, the authors [PERSON] and [PERSON] [61] focus on the concept of TomoSAR, pushing the limits of 3D imaging. They introduce us to the lifting diaphragm, a new concept that enhances our ability to rebuild reflective functions along the lifting direction. This echoes with the subject of advanced imaging techniques. [PERSON], [PERSON], and [PERSON] [62] suggest a complete semi-automatic processing chain for the reconstruction of 3D urban buildings, incorporating high-resolution SAR optic pairs. This seamless integration faces the practical challenge of rebuilding urban buildings and presents the need for a fusion cross-section. The spectral analysis approach described by [PERSON] and [PERSON] [63] treats the reversal of SAR as a spectral problem, emphasizing the role of hyper-analysis in the monitoring of urban infrastructure. The ability to distinguish multiple sources of scattering is vital to urban studies, contributing to continuing research in the field. In addition, [PERSON] and [PERSON] [64] emphasize the importance of the integration of SAR data with visual images because it is an example of the power of the combination of different imaging to create 3D information. This approach opens the doors to more complete and accurate 3D rebuilding. Synthetic aperture radar data are integrated with optical imagery to generate 3D information using stereogrammetric methods, as described by [PERSON], [PERSON] et al. [65]. The exploration of Polarimetric tomography SAR (Pol-Tomosar) performed by [PERSON], [PERSON], and [PERSON] [66] demonstrates its potential in urban applications by resolving multiple scatterers within the same analysis cell. This innovative technique immediately faces the need for increased accuracy in complex urban environments. Continuing the review in the field of synthetic radar, authors [PERSON], [PERSON] et al. [67] introduce the concept of Aetomo-Net, a visual network that uses multidimensional features for SAR tomography. This neuronal network highlights the growing role of artificial intelligence in the reconstruction of the tomographic image. By completing the search in this field, the discussion of the performance by [PERSON] [68] expands our exploration beyond SAR, offering information on seismic exploration applications. It highlights the interdisciplinary nature of tomographic imaging, providing valuable information on seismic studies. As we continue with an overview of the world's seismic tomography, [PERSON] [69] emphasizes the importance of quantitative interpretations in promoting the understanding of geodynamics. He emphasizes the transition from qualitative to quantitative approaches, reflecting the evolution in the field of tomography. [PERSON] and [PERSON] [70] introduced us to the utilization of cross-well seismic data, emphasizing the importance of the Fourier projection slice theorem and its role in characterizing the resolution and uniqueness of tomograms.