Perturbation-based Error Analysis of Iterative Image Reconstruction Algorithm for X-ray Computed Tomography

Statistical iterative image reconstruction methods are compute intensive. Fixed-point calculations can substantially reduce the computational load, but also increase quantization error. To investigate the effect of fixed-point quantization, we analyze the error propagation after introducing perturbation in a diagonally preconditioned gradient descent algorithm for X-ray computed tomography. The effects of the quantization error in forward-projection, back-projection, and image update are calculated using the open loop and loop gain of the iterative algorithm. We derive an analytical upper bound on the quantization error variance of the reconstructed image and show that the quantization step size can be chosen to meet a given upper bound. The analytical results are confirmed by numerical simulations.