Approximations of noise structures in helical multi-detector CT scans: application to lung nodule volume estimation

We have previously presented a match filtered (MF) approach for estimating lung nodule size from helical multi-detector CT (MDCT) images [1], in which we minimized the sum of squared differences between the simulated CT templates and the actual nodule CT images. The previous study showed the potential of this approach for reducing the bias and variance in nodule size estimation. However, minimizing SSD is not statistically optimal because the noise in 3D helical CT images is correlated. The goal of this work is to investigate the noise properties and explore several approximate descriptions of the three-dimensional (3D) noise covariance for more accurate estimates. The approximations include: variance only, noise power spectrum (NPS), axial correlation, two-dimensional (2D) in-plane correlation and fully 3D correlation. We examine the effectiveness of these second-order noise approximations by applying them to our volume estimation approach with a simulation study. Our simulations show that: the variance-based pre-whitening and axial pre-whitening perform very similar to the non-prewhitening case, with accuracy (measured in RMSE) differences within 1%; the NPS based pre-whitening performs slightly better, with a 4% decrease in RMSE; the in-plane pre-whitening and 3D fully pre-whitening perform best, with about a 10% decrease in RMSE over the non-prewhitening case. The simulation results suggest that the NPS, 2D in-plane and fully 3D prewhitening can be beneficial for lung nodule size estimation, albeit with greater computational costs in determining these noise characterizations.