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Study on analytical noise propagation in convolutional neural network methods used in computed tomography imaging

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Abstract

Neural network methods have recently emerged as a hot topic in computed tomography (CT) imaging owing to their powerful fitting ability; however, their potential applications still need to be carefully studied because their results are often difficult to interpret and are ambiguous in generalizability. Thus, quality assessments of the results obtained from a neural network are necessary to evaluate the neural network. Assessing the image quality of neural networks using traditional objective measurements is not appropriate because neural networks are nonstationary and nonlinear. In contrast, subjective assessments are trustworthy, although they are time- and energy-consuming for radiologists. Model observers that mimic subjective assessment require the mean and covariance of images, which are calculated from numerous image samples; however, this has not yet been applied to the evaluation of neural networks. In this study, we propose an analytical method for noise propagation from a single projection to efficiently evaluate convolutional neural networks (CNNs) in the CT imaging field. We propagate noise through nonlinear layers in a CNN using the Taylor expansion. Nesting of the linear and nonlinear layer noise propagation constitutes the covariance estimation of the CNN. A commonly used U-net structure is adopted for validation. The results reveal that the covariance estimation obtained from the proposed analytical method agrees well with that obtained from the image samples for different phantoms, noise levels, and activation functions, demonstrating that propagating noise from only a single projection is feasible for CNN methods in CT reconstruction. In addition, we use covariance estimation to provide three measurements for the qualitative and quantitative performance evaluation of U-net. The results indicate that the network cannot be applied to projections with high noise levels and possesses limitations in terms of efficiency for processing low-noise projections. U-net is more effective in improving the image quality of smooth regions compared with that of the edge. LeakyReLU outperforms Swish in terms of noise reduction.

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Authors and Affiliations

  1. Department of Engineering Physics, Tsinghua University, Beijing, 100084, China

    Xiao-Yue Guo, Li Zhang & Yu-Xiang Xing

  2. Key Laboratory of Particle and Radiation Imaging, Tsinghua University, Beijing, 100084, China

    Xiao-Yue Guo, Li Zhang & Yu-Xiang Xing

Authors
  1. Xiao-Yue Guo
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  2. Li Zhang
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  3. Yu-Xiang Xing
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by XYG, LZ, and YXX. The first draft of the manuscript was written by XYG and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Yu-Xiang Xing.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 62031020 and 61771279).

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Guo, XY., Zhang, L. & Xing, YX. Study on analytical noise propagation in convolutional neural network methods used in computed tomography imaging. NUCL SCI TECH 33, 77 (2022). https://doi.org/10.1007/s41365-022-01057-3

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  • DOI: https://doi.org/10.1007/s41365-022-01057-3

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