# Algorithms in Tomography and Related Inverse Problems--A Review
## 1 Introduction
### Tomographic Imaging: From SAR, Geology, to Medical Advances
This aligns with the theme of the theoretical foundations of tomographic imaging. [PERSON] and [PERSON] [71] discuss the critical role of X-ray computed tomography in the imaging of porosity, permeability, and fluid phase distribution in porous media. The importance of spatial resolution and adaptability in various flow conditions, connecting with the need for versatile imaging tools, is emphasized. The use of multistatic ground-penetrating radar signals, as analyzed by [PERSON], [PERSON] et al. [72], introduces a novel approach to tomographic imaging, particularly in the context of intensity distributions. This innovative approach highlights the need for adaptive imaging solutions. Subsequently, in the field of interdisciplinary and theoretical tomography, as mentioned by [PERSON] [73], a new interpretation of self-confident data highlights the need for innovative approaches to the interpretation of tomographic data. This is in line with the primary issue of pushing the boundaries of traditional imaging techniques. The introduction of 3 DInvNet by [PERSON], [PERSON] et al. [74] addresses the challenges of non-linearity and computational cost in 3D reconstruction algorithms. This innovative scheme demonstrates the evolving landscape of tomographic imaging techniques. Delving into the field of medical tomography, [PERSON] and [PERSON] [75] present efficient methods for ultrasound tomography with attenuation. This expands the horizons of tomographic imaging into the realm of medical diagnostics, emphasizing the role of sound wave attenuation in imaging. The application of ultrasound computed tomography in breast tissue imaging, as discussed by [PERSON], [PERSON], and [PERSON] [76], highlights the potential for quantitative 3D imaging. The introduction of finite-frequency travel-time tomography underscores the need for precision in medical tomographic applications. The exploration of non-interference three-dimensional refractive index tomography by [PERSON], [PERSON] et al. [77] highlights the application of tomographic imaging in the life science field. This approach focuses on simplicity and robust imaging performance, emphasizing the need for adaptability. The innovative deep prior diffraction tomography method introduced by [PERSON] and [PERSON] [78] offers a high-resolution reconstruction of refractive indices within dense biological samples. It demonstrates the potential of unconventional imaging methods in life sciences. [PERSON] [79] presents a fast method for reconstructing electron density in X-ray scanning applications. This approach aligns with the theme of efficient imaging solutions, particularly in scenarios dominated by Compton scattering. Finally, as highlighted by [PERSON], [PERSON] et al. [80], a multi-slice neural network with an optical structure presents the fusion of advanced technology with optical science. This innovative approach highlights the synergy between different disciplines. Optical Coherence Tomography is a cutting-edge technology used for non-invasive cross-sectional imaging within biological systems. This method utilizes low-coherence interferometry to create a two-dimensional image that reveals the way light scatters from internal tissue microstructures, much like how ultrasound pulse-echo imaging works. Optical Coherence Tomography provides incredibly precise longitudinal and lateral spatial resolutions, down to just a few micrometers, and has the capability to detect extremely faint reflected signals, as minute as approximately one-tenth of a billionth of the incoming optical power [81; 82; 83; 84]. In conclusion, whether in the domain of SAR, seismic exploration, medical diagnostics, or life sciences, these references underscore the dynamic nature of tomography and its ever-evolving role in diverse applications. The integration of advanced algorithms, artificial intelligence, and innovative methodologies reflects the continuous pursuit of higher image quality, precision, and efficiency.