An alternative solution to the nonuniform noise propagation problem in fan-beam FBP image reconstruction

It has been observed that the variances in reconstructed images from stationary noisy projection data by fan-beam filtered backprojection (fFBP) algorithm with ramp in the filtering step and linear interpolation in the backprojection step are nonuniform across the field-of-view. This is believed to be caused by the distance-dependent 1/L² factor in the fFBP reconstruction formula. Shift-variant filtration approach in the filtering step has been investigated to address the nonuniform noise propagation problem in fFBP. In this work, we present an alternative solution by the use of spatially variant weighting, instead of spatially invariant interpolation, in the backprojection step, while maintaining the homogeneous ramp filtering. Both theoretically predicted and empirically determined results concur and demonstrate the effectiveness of the presented alternative solution.