A geometric based preprocessing for weighted ray transforms with applications in SPECT

Abstract

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.