Technical Note: An Efficient Implementation of the Spherical Radon Transform with Cylindrical Apertures (2402.15641v1)
Abstract: The spherical Radon transform (SRT) is an integral transform that maps a function to its integrals over concentric spherical shells centered at specified sensor locations. It has several imaging applications, including synthetic aperture radar and photoacoustic computed tomography. However, computation of the SRT can be expensive. Efficient implementation of SRT on general purpose graphic processing units (GPGPUs) often utilizes non-matched implementation of the adjoint operator, leading to inconsistent gradients in optimization-based image reconstruction methods. This work details an efficient implementation of the SRT and its adjoint for the case of a cylindrical measurement aperture. Exploiting symmetry of the cylindrical geometry, the SRT can then be expressed as the composition of two circular Radon transforms (CRT). Utilizing this formulation then allows for an efficient implementation of the SRT as a discrete-to-discrete operator utilizing sparse matrix representation.
- N. J. Redding and T. M. Payne, “Inverting the spherical radon transform for 3d sar image formation,” in 2003 Proceedings of the International Conference on Radar (IEEE Cat. No. 03EX695). IEEE, 2003, pp. 466–471.
- J. Poudel, Y. Lou, and M. A. Anastasio, “A survey of computational frameworks for solving the acoustic inverse problem in three-dimensional photoacoustic computed tomography,” Physics in Medicine & Biology, vol. 64, no. 14, p. 14TR01, jul 2019. [Online]. Available: https://doi.org/10.1088/1361-6560/ab2017
- P. Burgholzer, G. J. Matt, M. Haltmeier, and G. Paltauf, “Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface,” Physical Review E, vol. 75, no. 4, p. 046706, 2007.
- P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Problems, vol. 23, no. 6, p. S65, 2007.
- Y. Zhou, J. Yao, and L. V. Wang, “Tutorial on photoacoustic tomography,” Journal of biomedical optics, vol. 21, no. 6, pp. 061 007–061 007, 2016.
- J. A. Fawcett, “Inversion of n-dimensional spherical averages,” SIAM Journal on Applied Mathematics, vol. 45, no. 2, pp. 336–341, 1985.
- Y. Lou, S. Park, F. Anis, R. Su, A. A. Oraevsky, and M. A. Anastasio, “Analysis of the use of unmatched backward operators in iterative image reconstruction with application to three-dimensional optoacoustic tomography,” IEEE Transactions on Computational Imaging, vol. 5, no. 3, pp. 437–449, 2019.
- M. Haltmeier and S. Moon, “The spherical radon transform with centers on cylindrical surfaces,” Journal of Mathematical Analysis and Applications, vol. 448, no. 1, pp. 567–579, 2017.
- P. C. Hansen and J. S. Jørgensen, “AIR Tools II: algebraic iterative reconstruction methods, improved implementation,” Numerical Algorithms, vol. 79, no. 1, pp. 107–137, 2018.
- J. R. Gilbert, C. Moler, and R. Schreiber, “Sparse matrices in MATLAB: Design and implementation,” SIAM journal on matrix analysis and applications, vol. 13, no. 1, pp. 333–356, 1992.
- L. Lozenski and U. Villa, “SRT for Cylindrical Apertures,” 2024. [Online]. Available: {https://doi.org/10.5281/zenodo.10694898}
- ——, “Neural Field CRT Dynamic Imaging,” 2022. [Online]. Available: {https://doi.org/10.5281/zenodo.7007589}