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

Abstract

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. Compared to the empirical variance derived from multiple simulated reconstruction realizations, our method is as accurate as the currently available methods of variance prediction while being computable for thousands of voxels per second, faster than these previous methods by a factor of over ten thousand. We also compare our method to empirical variance maps produced from an ensemble of reconstructions from real sinogram data. The LFR can also be used to predict the power spectrum of the noise and the local frequency response of the reconstruction.

Tube current modulation (TCM), the redistribution of X-ray dose in CT between different views of a patient, has been demonstrated to reduce dose when the modulation is well-designed. TCM methods currently in use were designed assuming FBP-based image reconstruction. We use our LFR approximation to derive fast methods for predicting the SNR of linear observers of a statistically reconstructed CT image. Using these fast observability and variance prediction methods, we derive TCM methods specific to statistical reconstruction that, in theory, potentially reduce radiation dose by 20% compared to FBP-specific TCM methods.