Fast Variance Prediction for Iteratively Reconstructed CT with Applications to Tube Current Modulation

X-ray computed tomography (CT) is an important, widely-used medical imaging modality. A primary concern with the increasing use of CT is the ionizing radiation dose incurred by the patient. Statistical reconstruction methods are able to improve noise and resolution in CT images compared to traditional filter backprojection (FBP) based reconstruction methods, which allows for a reduced radiation dose. Compared to FBP-based methods, statistical reconstruction requires greater computational time and the statistical properties of resulting images are more difficult to analyze. Statistical reconstruction has parameters that must be correctly chosen to produce high-quality images. The variance of the reconstructed image has been used to choose these parameters, but this has previously been very time-consuming to compute.

In this work, we use approximations to the local frequency response (LFR) of CT projection and backprojection to predict the variance of statistically reconstructed CT images. Our method is as accurate as the currently available methods of variance prediction while being computable for thousands of voxels per second, several orders of magnitude faster than these previous methods. We also compare our method to empirical variance maps produced from an ensemble of reconstructions from real sinogram data. Finally, we derive methods for modulating the X-ray tube current during a CT scan that potentially allow further dose reduction.