Abstract
In this work we investigate numerically the reconstruction approach proposed in [F. O. Goncharov and R. G. Novikov, An analog of Chang inversion formula for weighted Radon transforms in multidimensions, Eurasian J. Math. Comput. Appl. 4 2016, 2, 23–32] for weighted ray transforms (weighted Radon transforms along oriented straight lines) in 3D. In particular, the approach is based on a geometric reduction of the data modeled by weighted ray transforms to new data modeled by weighted Radon transforms along two-dimensional planes in 3D. Such reduction could be seen as a preprocessing procedure which could be further completed by any preferred reconstruction algorithm. In a series of numerical tests on modelized and real SPECT (single photon emission computed tomography) data we demonstrate that such procedure can significantly reduce the impact of noise on reconstructions.
A A few remarks on implementations
There were only two crucial steps for our numerical implementations:[1]
Numerical implementation of formulas (2.5) and (2.6) for reduction of
Inversion of classical Radon transform R for
Acknowledgements
The materials for the present work were obtained in the framework of research conducted under the direction of Professor R. G. Novikov. I am also very grateful for the comments and remarks of professor L. Kunyansky during the conference AIP-2019 and also during the author’s thesis defense procedure. Also I would like to express my gratitude to J.-P. Guillement from Université de Nantes for providing codes for SPECT reconstructions in 2D and for related discussions on numerical methods in SPECT.
References
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