FBP algorithms for attenuated fan-beam projections

Filtered backprojection (FBP) reconstruction algorithm for attenuated fan-beam projections has been derived based on Novikov's inversion formula. The filtering is shift-invariant. The derivation uses a relation of partial derivative between the Cartesian and polar coordinates. We implemented the FBP algorithm and presented the numerical results. As a special application, we give a shift-invariant FBP algorithm for fan-beam SPECT reconstruction with uniform attenuation compensation. Some additional equivalent fan-beam algorithms are also discussed. In the attenuation-free case, our algorithm reduces to the conventional fan-beam FBP algorithm.