An Analytical Solution for Backscatter Tomography

We utilize the Novikov-Natterer algorithm for non-uniform attenuation to invert the backscatter projections formed by the scatter of X-rays. The backscatter signal is treated as an emitter in a non-uniformly attenuating medium. This type of tomography has applications in radiology and dentistry for which metals effectively block the transmission of X-rays. Scanning for metals also has applications in security/baggage screening. The results show that when the forward scattering angle is zero, the algorithm, with a redefinition of the density function f , reduces to the PET attenuation correction.