Rapidly converging image covariance estimation for FBP reconstruction methods

We propose a new estimator for covariance between pixels in x-ray CT images reconstructed using algorithms of the filtered backprojection type. Our new estimator is unbiased and is found to have significantly lower variance than the conventional unbiased estimator. We demonstrate the accuracy of our new estimator for both fan-beam and cone-beam reconstruction via Monte Carlo simulation. Moreover, we provide an analytical expression for the estimator variance and verify it numerically with Monte Carlo simulation.