Fig 1.
The architecture of the proposed deep learning reconstruction framework for X-CT with incomplete projections.
For each three-dimensional block, the height and width represent the feature map’s size and the depth corresponds to the number of channels in this feature map.
Fig 2.
The working principles of the max-pooling operator and the convolutional filter.
Table 1.
The values of the parameters in the deep learning layers.
Fig 3.
The sparse-view results of one synthetic phantom with an incomplete sinogram with 90 views by using DCNN [32], FBP and DLFBP.
The incomplete singoram has a size of 90 × 731 pixels. The corrupted sinograms generated by the forward projection have a size of 720 × 731 pixels. All CT images have a size of 512 × 512 pixels after cutting off the surrounding blank region. Some regions of these images, indicated by the yellow box, are enlarged for better visualization.
Fig 4.
The sparse-view results of one synthetic phantom with an incomplete sinogram with 60 views by using DCNN [32], FBP and DLFBP.
The incomplete singoram has a size of 60 × 731 pixels. The corrupted sinograms generated by the forward projection have a size of 720 × 731 pixels. All CT images have a size of 512 × 512 pixels after cutting off the surrounding blank region. Some regions of these images, indicated by the yellow box, are enlarged for better visualization.
Fig 5.
The sparse-view results of one head slice with an incomplete sinogram with 90 views by using DCNN [32], FBP and DLFBP.
The incomplete singoram has a size of 90 × 731 pixels. The corrupted sinograms generated by the forward projection have a size of 720 × 731 pixels. All CT images have a size of 512 × 512 pixels after cutting off the surrounding blank region. Some regions of these images, indicated by the yellow box, are enlarged for better visualization.
Fig 6.
The sparse-view results of one head slice with an incomplete sinogram with 60 views by using DCNN [32], FBP and DLFBP.
The incomplete singoram has a size of 60 × 731 pixels. The corrupted sinograms generated by the forward projection have a size of 720 × 731 pixels. All CT images have a size of 512 × 512 pixels after cutting off the surrounding blank region. Some regions of these images, indicated by the yellow box, are enlarged for better visualization.
Fig 7.
The PSNR values of the sparse-view CT images.
The blue points with circle masks present the PSNR values of the CT images reconstructed by FBP. The orange points with rhombus masks present the PSNR values of the results by DLFBP. The gray points with square masks present the PSNR values of the results by DCNN [32].
Table 2.
aPSNR values of sparse-view results.
Fig 8.
The limited-angle results of one synthetic phantom with the projections within the angular range [0 120°] by using DCNN [32], FBP and DLFBP.
The incomplete singoram has a size of 240 × 731 pixels. The corrupted sinograms generated by the forward projection have a size of 720 × 731 pixels. All CT images have a size of 512 × 512 pixels after cutting off the surrounding blank region. Some regions of these images, indicated by the yellow box, are enlarged for better visualization.
Fig 9.
The limited-angle results of one synthetic phantom with the projections within the angular range [0 90°] by using DCNN [32], FBP and DLFBP.
The incomplete singoram has a size of 180 × 731 pixels. The corrupted sinograms generated by the forward projection have a size of 720 × 731 pixels. All CT images have a size of 512 × 512 pixels after cutting off the surrounding blank region. Some regions of these images, indicated by the yellow box, are enlarged for better visualization.
Fig 10.
The limited-angle results of one head slice with the projections within the angular range [0 120°] by using DCNN [32], FBP and DLFBP.
The incomplete singoram has a size of 240 × 731 pixels. The corrupted sinograms generated by the forward projection have a size of 720 × 731 pixels. All CT images have a size of 512 × 512 pixels after cutting off the surrounding blank region. Some regions of these images, indicated by the yellow box, are enlarged for better visualization.
Fig 11.
The limited-angle results of one head slice with the projections within the angular range [0 90°] by using DCNN [32], FBP and DLFBP.
The incomplete singoram has a size of 180 × 731 pixels. The corrupted sinograms generated by the forward projection have a size of 720 × 731 pixels. All CT images have a size of 512 × 512 pixels after cutting off the surrounding blank region. Some regions of these images, indicated by the yellow box, are enlarged for better visualization.
Fig 12.
The PSNR values of the limited-angle CT images.
The blue points with circle masks present the PSNR values of the CT images reconstructed by FBP. The orange points with rhombus masks present the PSNR values of the results by DLFBP. The gray points with square masks present the PSNR values of the results by DCNN [32].
Table 3.
aPSNR values of limited-view results.
Table 4.
aPSNR values of different down-sampling methods.