Inversion of the Attenuated X-Ray Transforms: Method of Riesz Potentials

Abstract EN

The attenuated X-ray transform arises from the image reconstruction in single-photon emission computed tomography.

The theory of attenuated X-ray transforms is so far incomplete, and many questions remain open.

This paper is devoted to the inversion of the attenuated X-ray transforms with nonnegative varying attenuation functions μ, integrable on any straight line of the plane.

By constructing the symmetric attenuated X-ray transform Aμ on the plane and using the method of Riesz potentials, we obtain the inversion formula of the attenuated X-ray transforms on Lpℝ21≤p<2 space, with nonnegative attenuation functions μ, integrable on any straight line in ℝ2.

These results are succinct and may be used in the type of computerized tomography with attenuation.