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 nonsta-tionary and nonlinear.In contrast,subjective assessments are trustworthy,although they are time-and energy-con-suming for radiologists.Model observers that mimic sub-jective assessment require the mean and covariance of images,which are calculated from numerous image sam-ples;however,this has not yet been applied to the evalu-ation 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,demon-strating that propagating noise from only a single projec-tion is feasible for CNN methods in CT reconstruction.In addition,we use covariance estimation to provide three measurements for the qualitative and quantitative perfor-mance 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 com-pared with that of the edge.LeakyReLU outperforms Swish in terms of noise reduction.

Xiao-Yue Guo;Li Zhang;Yu-Xiang Xing

Department of Engineering Physics,Tsinghua University,Beijing 100084,China;Key Laboratory of Particle and Radiation Imaging,Tsinghua University,Beijing 100084,China

核技术（英文版）

[1]Xiao-Yue Guo;Li Zhang;Yu-Xiang Xing-.Study on analytical noise propagation in convolutional neural network methods used in computed tomography imaging)[J].核技术（英文版）,2022(06):114-127

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