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Deep learning-based image denoising and reconstruction methods have shown promising results for low-dose CT. When high-quality reference images are not available for training the network, researchers found a powerful and effective counterpart called Noise2Noise, which trains the neural network using paired data with independent noise. However, it is uncommon to have paired CT scans with independent noise (e.g., from two scans). In this paper, a method is proposed to generate such paired data for potential usage in deep learning training by simultaneously simulating a low-dose image at arbitrary dose level and an image with independent noise from a single CT scan. Their independence is investigated both analytically and numerically. In our numerical study, a Shepp-Logan phantom was utilized in MATLAB to generate the ground-truth, normal-dose, and low-dose images for reference. Noise images were obtained for analysis by subtracting the ground-truth from the noisy images, including the normal-dose/low-dose images and the paired products of our proposed method. Our numerical study matches the analytical results very well, showing that the paired images are not correlated. Under an additional assumption that they form a bivariate normal distribution, they are also independent. The proposed method can produce a series of paired images at arbitrary dose level given one CT scan, which provides a powerful new method to enrich the diversity of low-dose data for deep learning.
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