Fig. 1. Attenuation process of X-ray penetrating an object
[18] Fig. 2. Schematic of beam projection
[19]. (a) Radon transform-based parallel beam projection process; (b) sectoral beam projection process
Fig. 3. Schematic of the CT reconstruction process
[21] Fig. 4. Visual of reconstructed CT degradation. (a) Full dose reference CT image; (b) full-view (180°) reconstructed CT image; (c) 1/6 sampling sparse-view reconstructed CT image; (d) reconstructed CT image under limited-angle of [0, 120°]
Fig. 5. CNN
[25]. (a) Basic structure of CNN; (b) basic structure of neurons of a neural network
Fig. 6. Embedding modules in CNN. (a) Residual network module
[29]; (b) dense connection module
[30]; (c) channel attention module
[31]; (d) spatial attention module
[32] Fig. 7. CT image domain post-processing process
Fig. 8. Network structure and comparison of reconstruction results
[43]. (a) U-net based on multi-level wavelet transform; (b) comparison of CT reconstruction results
Fig. 9. Artifact removal model combining TV regularization iteration reconstruction with U-net
[47] Fig. 10. Artifact removal models based on GAN or DDPM. (a) U-WGAN model
[53]; (b) DDPM
[55] Fig. 11. Reconstruction results of the artifact removal models based on GAN or DDPM. (a) CT reconstruction results in Ref. [
53]; (b) CT reconstruction results in Ref. [
55]
Fig. 12. FCN artifact removal models based on different network structures. (a) R2-Net model
[59]; (b) MS-RDN model
［64］ Fig. 13. Artifact removal model based on Transformer
[69] Fig. 14. Sinogram domain preprocessing process
Fig. 15. Sinogram interpolation models based on U-net. (a) Model combining linear interpolation with U-net
[72]; (b) DPC-CT model
[75] Fig. 16. Sinogram interpolation models based on GAN. (a) CT-Net model
[76]; (b) SI-GAN model
[80] Fig. 17. Reconstruction results of the sinogram interpolation models based on GAN. (a) CT reconstruction results in Ref. [
76];
Fig. 18. Dual-domain network joint processing process
Fig. 19. Dual-domain reconstruction network based on U-net and FCN. (a) SPID model
[84]; (b) multi-channel sinogram restoration model
[86]; (c) DuDoDR-Net model
[87] Fig. 20. Reconstruction results of dual-domain reconstruction networks based on U-net and FCN. (a) CT reconstruction results in Ref. [
84]; (b) CT reconstruction results in Ref. [
86]; (c) CT reconstruction results in Ref. [
87]
Fig. 22. Network structure and reconstruction results
[102]. (a) Dual-domain reconstruction network based on Transformer; (b) comparison of CT reconstruction results
Fig. 23. CNN regular term based iterative reconstruction process
[103] Fig. 24. Optimization model of regular terms and balance parameters based on CNN and reconstruction results
[108]. (a) RegFormer model; (b) comparison of CT reconstruction results
Fig. 25. Sub-problem iterative expansion optimization models based on CNN. (a) FISTA-based iterative reconstruction model
[112]; (b) shear wave based iterative reconstruction model
[113] Fig. 26. Reconstruction results of sub-problem iterative expansion optimization model based on CNN. (a) CT reconstruction results in Ref. [
112]; (b) CT reconstruction results in Ref. [
113]
Fig. 27. Unsupervised iterative model and reconstruction results
[120]. (a) REDAEP iterative reconstruction model; (b) comparison of CT reconstruction results
Fig. 28. End-to-end mapping reconstruction process
Fig. 29. Full-learning reconstruction model. (a) Reconstruction network based on fully connected layer
[124-125]; (b) reconstruction network based on stacked U-net
[128] Fig. 30. Reconstruction results of full-learning reconstruction models. (a) CT reconstruction results in Ref. [
125];
Fig. 31. Reconstruction model based on learnable physical analytic algorithm and comparison of reconstruction results
[130]. (a) iRadonMAP model; (b) comparison of CT reconstruction results
Fig. 32. Self-supervised untrained projection reconstruction model and reconstruction results
[137]. (a) IntraTomo model; (b) comparison of CT reconstruction results
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［40］ | Residual learning， skip connection | MSE | Biomedical，Ellipsoidal，Human Knee | Advantages： artifact removal in different frequency bands and simple implementation Limitations： the network structure and loss function are single | | ［41-42］ | Residual learning， skip connection， wavelet transform | MSE | AAPM Low Dose CT | | ［43］ | Residual learning， skip connection， wavelet transform | | Chest and Catphan phantom | | ［44］ | Skip connection | MAE | 3D Spectral Slices | | ［45-46］ | Residual learning， skip connection | | TCIA | | ［47］ | Residual learning， skip connection | SSIM loss | AAPM Low Dose CT |
|
Table 1. Summary of artifact removal model based on U-net
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［48］ | Residual learning | GAN loss， perceptual loss | Human Knee | Advantages： the resulting CT images are rich in detail and DDPM is more controllable；DDPM models do not require labels Limitations： GANs are difficult to train and have poor convergence；the sampling speed of DDPM is slow | | ［49］ | Skip connection | GAN loss，MSE | TCGA-CESC | | ［50］ | Residual learning， skip connection | MAE，MSE | TCIA | | ［52］ | Skip connection | Wasserstein loss，MSE | Dental CT | | ［53］ | Dense block， skip connection | Wasserstein loss，MSE， SSIM loss | AAPM Low Dose CT | | ［54］ | DDPM | MSE，KL divergence | Checked-in Luggage，C4KC-KiTS | | ［55］ | DDPM | MSE，KL divergence | LIDC，LDCT |
|
Table 2. Summary of artifact removal model based on GAN or DDPM
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［57］ | Dense block， skip connection | MSE，MS-SSIM loss | NBIA | Advantages： design different network structures according to task requirements and data characteristics and the reconstruction algorithm is fast Limitations： the loss function is single | | ［58］ | Residual learning，GoogLeNet | MSE | Clinical Routine CT | | ［59］ | Residual learning，channel attention，recursive transformer | MSE | AAPM Low Dose CT | | ［60］ | Multi-scale dilated convolution，multi-scale pooling | | LiTS | | ［61］ | Multi-scale dilated convolution，Clique Block［62］ | MSE | AAPM Low Dose CT | | ［63］ | Residual learning | MAE | LIDC-IDRI | | ［64］ | Dense block， residual learning | MAE | Breast CT | | ［65］ | Dense block， residual learning | MAE | Head CT | | ［66］ | Residual learning， skip connection | MSE | AAPM Low Dose CT | | ［67］ | Skip connection | MSE | 4D-Lung，DIR-LAB |
|
Table 3. Summary of artifact removal model based on other FCN
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［70］ | Residual learning | | XCAT | Advantages： the network structure design is simple and the network operation efficiency is high | | ［71］ | Residual learning，skip connection | MSE | Lung CT | | ［72］ | Residual learning，skip connection | MSE | micro-CT | | ［73］ | Residual learning，skip connection | | | Limitations： the loss function is single | | ［74］ | Skip connection | MSE | Phantoms | | ［75］ | Skip connection，dense block， residual learning | MSE， MS-SSIM loss | Phantoms |
|
Table 4. Summary of sinogram interpolation model based on U-net and FCN
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［76］ | 1D convolution | MSE，GAN loss | Checked in luggage CT | Advantages： generate complete projection data at extreme sparse views and have high feature similarity Limitations： GANs are difficult to train and have poor convergence | | ［77］ | Skip connection | MSE，GAN loss | Siemens Somatom CT | | ［78］ | Residual learning，skip connection | MSE，GAN loss | Oral CT | | ［79］ | Skip connection | MAE，GAN loss | Cranial cavity CT | | ［80］ | Skip connection | MAE，GAN loss | Cranial cavity CT，Head PhantomCT | | ［82］ | Skip connection， residual learning | MAE，GAN loss | Modified FORBILD abdomen phantom CT | | ［83］ | Skip connection | MSE，GAN loss | AAPM Low Dose CT |
|
Table 5. Summary of sinogram interpolation model based on GAN
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［84］ | Residual learning，skip connection | MSE，TV loss | AAPM Low Dose CT | Advantages： the network has dual domain data fidelity； end-to-end reconstruction of projection data | | ［85］ | Residual learning，skip connection，wavelet transform | MAE | TCIA | | ［86］ | Residual learning，skip connection | MSE | thoracic CT | | ［87］ | Dense block，channel attention，residual learning，skip connection | MAE | DeepLesion | | ［88］ | Residual learning | MAE，MSE | AAPM Low Dose CT | | ［89］ | Skip connection | MSE | AAPM Low Dose CT | | ［90］ | Residual learning，skip connection，dual channel fusion | MAE，SSIM loss，DIFF loss | AAPM Low Dose CT | | ［91］ | Residual learning，skip connection | | Small animal Xtrim PET | | ［92］ | Skip connection | MSE | AAPM Low Dose CT | | ［93］ | Skip connection | Cross-entropy loss | Xenopus kidney embryos | | ［94］ | Skip connection | MSE | real 9-view CT EDS | | ［95］ | Residual learning，skip connection | MSE | AAPM Low Dose CT | | ［96］ | Residual learning | MSE，GAN loss， Perceptual loss | Data Science Bowl 2017 | Limitations： dual CNN structure is simple；dual GANs further increase the cost of training and the difficulty of convergence | | ［97］ | Skip connection | MAE，GAN loss | Heart craniocaudally CT | | ［98］ | Skip connection，cosine similarity，Softmax attention | Hole_L1 loss，perceptual loss，Cycle GAN loss | DeepLesion，LDCT and Projection data |
|
Table 6. Summary of dual-domain reconstruction network based on CNN and GAN
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［99］ | Swin-Transformer | MSE | AAPM Low Dose CT | Advantages： long-range dependency modeling capability； extracting global feature information Limitations： large number of parameters of the self-attention mechanism | | ［100］ | Transformer | MSE | LIDC-IDRI | | ［101］ | Swin-Transformer | MSE，Charbonnier loss | LDCT and Projection data | | ［102］ | Swin-Transformer，Sobel operator | MSE | AAPM Low Dose CT |
|
Table 7. Summary of dual-domain reconstruction network based on Transformer
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［103］ | Residual learning | MSE | AAPM Low Dose CT | Advantages： avoid the selection of regular terms and balance parameters； reduce the cost of manual experiments and computational complexity Limitations： high number of reconstruction iterations | | ［104］ | Residual learning | MSE，perceptual loss | AAPM Low Dose CT | | ［105］ | 1D convolution | MSE | | | ［106］ | Residual learning | MSE | Ellipses，head phantom | | ［107］ | Residual learning，skip connection | MSE | TCIA | | ［108］ | Transformer | MSE | AAPM Low Dose CT |
|
Table 8. Summary of optimization model of regular terms and balance parameters based on CNN
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［109］ | Convolution-based | MSE | AAPM Low Dose CT，Clinical Head | Advantages： mapping solutions to non-convex problem； accelerated reconstruction rate using CNN Limitations： few parameters for network training； high number of reconstruction iterations | | ［110］ | Convolution-based | MSE，SSIM loss， semantic loss | AAPM Low Dose CT | | ［111］ | Convolution-based | MSE | AAPM Low Dose CT | | ［112］ | Residual learning | MSE | Simulated EMT | | ［113］ | Skip connection | MSE | Ellipses，AAPM Low Dose CT | | ［114］ | Skip connection | MSE | AAPM Low Dose CT | | ［115］ | Residual learning，skip connection | MSE，SSIM loss | AAPM Low Dose CT |
|
Table 9. Summary of the sub-problem iterative expansion optimization model based on CNN
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［116］ | Residual learning，skip connection | Wasserstein loss，MSE | NBIA | Advantages： attention mechanism increases reconstruction accuracy；unsupervised training reduces dependence on labeled data and provides greater generalization Limitations： attention mechanism increases network calculation parameters and reduces reconstruction speed；unsupervised network optimization is difficult | | ［117］ | Dense block， residual learning， channel and spatial attention | MSE | AAPM Low Dose CT，DeepLesion | | ［118］ | Residual learning | MSE | Chest and abdomen CT | | ［119］ | Fully connected | MSE，TV loss | AAPM Low Dose CT | | ［120］ | Residual learning | MSE | Ellipses，Chest CT | | ［121］ | Convolutional analysis operator learning | MSE | XCAT |
|
Table 10. Summary of other CNN iterative expansion and unsupervised iterative reconstruction models
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| ［122］ | Fully connected | MSE | Human FDG PET | Advantages： the algorithm design is simple to implement；does not require CT reconstruction expertise Limitations： low reconstruction accuracy；large number of parameters in the fully connected layer | | ［123］ | Fully connected | MSE | | | ［124-125］ | Fully connected | MSE | AAPM Low Dose CT | | ［126］ | Fully connected，residual learning，multi-channel fusion | MSE | TCGA-ESCA | | ［127］ | Skip connection | MSE | Shepp-Logan phantom，Forbild phantom | | ［128］ | Skip connection | MSE | |
|
Table 11. Summary of full-learning reconstruction model based on neural network
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| [129] | Fully connected | MSE | AAPM Low Dose CT | Advantages： incorporates physical reconstruction process；reduced model parameters Limitations： reconstruction accuracy and network structure need further optimization | | [130] | Fully connected，residual learning | MSE | AAPM Low Dose CT | | [131] | Residual learning，upsampling and downsampling block | MSE | AAPM Low Dose CT | | [132] | Hard shrinkage operator， multi-channel fusion | MSE | Coronary artery，abdomen CT | | [133] | Skip connection | SSIM loss，MAE，Wasserstein loss | Breast CT |
|
Table 12. Summary of reconstruction model based on learnable physical analytic algorithm
| Reference | Network detail | Loss function | Dataset | Feature |
|---|
| [134] | Convolution-based | MSE | Multi-grain structures CT | Advantages： network training does not depend on label；greater generalization of self-supervised networks Limitations： self-supervised network reconstruction process requires optimized weights resulting in long reconstruction time；the accuracy of untrained network reconstruction is still relatively low | | [135] | LSTM，residual learning，skip connection | MSE， Profiles loss，GAN loss | AAPM Low Dose CT | | [137] | Fourier feature projection layer，full connected | MSE | Logan phantom，ATLAS，Covid-19，SL and LoDoPaB-CT，Pepper，Rose | | [138] | Fourier feature projection layer，full connected | MSE | XCAT， AAPM Low Dose CT | | [139] | Convolution-based | MSE，TV loss | Shepp-Logan phantom，LIDC-IDRI，random ellipses |
|
Table 13. Summary of unsupervised or self-supervised end-to-end reconstruction models
| Application problem | Network structure | Iuput-Output | Advantage | Limitation |
|---|
| Image post-processing | FCN，GAN，U-net， Transformer，DDPM | CT-CT | Adaptive artifact removal；simple and doable | Lack of fidelity to the sinograms，MSE loss leads to structural ambiguity | Sinogram pre-processing | FCN，GAN，U-net | Sinogram-Sinogram | Adaptive interpolation；simple and doable | Lack of fidelity to CT images；may introduce tiny false structures | Dual-domain data processing | FCN，GAN，U-net，Transformer | Sinogram-CT | End-to-end reconstruction；dual-domain data fidelity | The existing model structure is relatively simple；increased amount of computation | | Iterative reconstruction | FCN，GAN，U-net，Transformer | Sinogram/CT-CT | Reduce the computational complexity and labor experiment costs | The process of iterating multiple times cannot be avoided；the reconstruction time is still long | | End-to-end mapping reconstruction | MLP，FCN，GAN， U-net | Sinogram-CT | MLP or CNN mapping method is simple to design；the learnable analytical reconstruction algorithm has a physical process guidance | MLP or CNN mapping methods lack physical reconstruction process and the reconstruction accuracy is not high |
|
Table 14. Applications of sparse-view or limited-angle CT reconstruction based on deep learning
![Attenuation process of X-ray penetrating an object[18]](/richHtml/lop/2023/60/8/0811002/img_01.jpg)
![Schematic of beam projection[19]. (a) Radon transform-based parallel beam projection process; (b) sectoral beam projection process](/richHtml/lop/2023/60/8/0811002/img_02.jpg)
![Schematic of the CT reconstruction process[21]](/Images/icon/loading.gif){kind=icon}
