Band-restricted estimation of noise variance in filtered backprojection reconstructions using repeated scans

We introduce a new estimator for noise variance in tomographic images reconstructed using algorithms of the filtered backprojection type. The new estimator operates on data acquired from repeated scans of the object under examination, is unbiased, and is shown to have significantly lower variance than the conventional unbiased estimator for many scenarios of practical interest. We provide an extensive theoretical analysis of this estimator, highlighting the circumstances under which it is most effective. This analysis includes both general and specific data-correlation patterns. Moreover, we have applied our estimator to real X-ray computed tomography data and present preliminary results that support the theory and provide experimental evidence of the new estimator's efficacy.