For the shortcomings of poor interpretation ability and instability in neural network training， a Chambolle- Pock （CP） algorithm optimized denoising network based on Total Variational （TV） regularization， CPTV-Net， was proposed to solve the denoising problem of Low-Dose Computed Tomography （LDCT） images. Firstly， the TV constraint term was introduced into the L1 regularization term model to preserve the structural information of the image. Secondly， the CP algorithm was used to solve the denoising model and obtain specific iterative steps to ensure the convergence of the algorithm. Finally， the shallow CNN （Convolutional Neural Network） was used to learn the iterative formula of the primal dual variables of the linear operation. The neural network was used to calculate the solution of the model， and the network parameters were collected to optimize the combined data. The experimental results on simulated and real LDCT datasets show that compared with five advanced denoising methods such as REDCNN （Residual Encoder-Decoder Convolutional Neural Network） and TED-Net （Transformer Encoder-decoder Dilation Network）， CPTV-Net has the best Peak Signal-to-Noise Ratio （PSNR）， Structural SIMilarity （SSIM）， and Visual Information Fidelity （VIF） evaluation values， and can generate LDCT images with significant denoising effect and the most details preserved.

Concerning the problems of artifacts and loss of image details in the analytically reconstructed image by time-domain filters， a new time-frequency domain Computed Tomography （CT） reconstruction algorithm based on Convolutional Neural Network （CNN） was proposed. Firstly， a filter network based on a convolutional neural network was constructed in the frequency domain to achieve the frequency-domain filtering of the projection data. Secondly， the back-projection operator was used to perform domain conversion on the frequency-domain filtered result to obtain a reconstructed image. A network was constructed in the image domain to process the image from the back-projection layer. Finally， a multi-scale structural similarity loss function was introduced on the basis of the minimum mean square error loss function to form a composite loss function， which reduced the blur effect of the neural network on the result image and preserved the details of the reconstructed image. The image domain network and the projection domain filter network worked together to finally get the reconstructed result. The effectiveness of the proposed algorithm was verified on the clinical dataset. Compared with the Filtered Back Projection （FBP） algorithm， the Total Variation （TV） algorithm and the image domain Residual Encoder-Decoder CNN （RED-CNN） algorithm， when the number of projections is respectively 180 and 90， the proposed algorithm achieved the reconstructed result image with highest Peak Signal-to-Noise Ratio （PSNR） and Structural Similarity （SSIM）， and the least Normalized Mean Square Error （NMSE）.When the number of projections is 360，the proposed algorithm is second only to TV algorithm. The experimental results show that the proposed algorithm can improve the reconstructed image quality of CT image， and it is feasible and effective.