Pixel-wise estimation of noise statistics on iterative CT reconstruction from a single scan

As iterative CT reconstruction continues to advance, the spatial distribution of noise standard deviation (STD) and accurate noise power spectrum (NPS) on the reconstructed CT images become important for method evaluation as well as optimization of algorithm parameters. Using a single CT scan, we propose a practical method for pixel-wise calculation of noise statistics on an iteratively reconstructed CT image, which enables accurate calculation of noise STD for each pixel and NPS.

We first derive the noise propagation from measured projections to an iteratively reconstructed CT image provided that the projection noise is known. We then show that the model of noise propagation remains approximately unchanged for extra simulated noise added on the measured projections. To compute the noise STD map and the NPS map on an iteratively reconstructed CT image from a single scan, we first iteratively reconstruct the CT image from the measured projections using an existing reconstruction algorithm. The same measured projections are added by different sets (a total of 32 sets in our implementation) of projection noise simulated from an estimated projection noise model, and are then used to iteratively reconstruct different CT images. The calculations of the noise STD map and the NPS map are finally performed on the entire stack of these different reconstruction images.

We evaluate our method on an anthropomorphic head phantom, and demonstrate the clinical utility on a set of head and neck patient CT data, using two iterative CT reconstruction algorithms: the penalized weighted least-square (PWLS) algorithm and the total-variation (TV) regularization. In the head phantom case, repeated scans are acquired to generate the ground truths of noise STD and NPS maps. Using only one single scan, the proposed method accurately calculates the noise STD maps with a root-mean-square error (RMSE) of less than 5HU. In the NPS map estimation, we compare the result of our proposed method with that of the conventional method which calculates the NPS maps on a uniform region of interest on one CT image. Our method outperforms the conventional method on the NPS map estimation with RMSE reduced by 92%. The implementation of the proposed method on the patient data successfully provides the noise STD values around complex structures and a high-quality NPS map.

The proposed method accurately calculates noise STD for each pixel and NPS on an iteratively reconstructed CT image, with no requirement of repeated CT scans. It provides a detailed evaluation of imaging performance of different iterative reconstruction methods on the same CT dataset.