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Deep-neural-network based sinogram synthesis for sparse-view CT image reconstruction
Hoyeon Lee, Jongha Lee, Hyeongseok Kim, Byungchul Cho, Seungryong Cho
TL;DR
Sparse-view CT reduces measurements but makes reconstruction ill-posed and vulnerable to streak or parameter-dependent artifacts. This paper uses a CNN-based sinogram synthesis method trained on real-patient CT data, and reports better reconstruction metrics for its U-Net than tested alternatives. The authors conclude that CNN synthesis can produce reconstructed images comparable to those from fully sampled sinograms.
Problem
Sparse-view CT reconstruction must recover missing data while avoiding the artifacts and parameter dependence associated with direct analytic or iterative reconstruction.
Method
The paper trains CNNs, including a residual U-Net, to synthesize missing sparse-view sinogram data from reprojected real-patient CT images.
Results
The proposed U-Net had the best NRMSE, PSNR, and SSIM among tested methods and showed the least streak artifacts in reconstructed images.
Takeaways & Limitations
CNN-based sinogram synthesis can effectively fill missing sparse-view data and produce reconstructed images comparable to those from fully sampled sinograms.
Abstract
from arXiv · showhide
Recently, a number of approaches to low-dose computed tomography (CT) have been developed and deployed in commercialized CT scanners. Tube current reduction is perhaps the most actively explored technology with advanced image reconstruction algorithms. Sparse data sampling is another viable option to the low-dose CT, and sparse-view CT has been particularly of interest among the researchers in CT community. Since analytic image reconstruction algorithms would lead to severe image artifacts, various iterative algorithms have been developed for reconstructing images from sparsely view-sampled projection data. However, iterative algorithms take much longer computation time than the analytic algorithms, and images are usually prone to different types of image artifacts that heavily depend on the reconstruction parameters. Interpolation methods have also been utilized to fill the missing data in the sinogram of sparse-view CT thus providing synthetically full data for analytic image reconstruction. In this work, we introduce a deep-neural-network-enabled sinogram synthesis method for sparse-view CT, and show its outperformance to the existing interpolation methods and also to the iterative image reconstruction approach.
I. INTRODUCTION
Sparse-view CT reduces ray measurements but creates an ill-posed reconstruction problem with artifacts and unresolved questions about clinically acceptable sampling. The paper addresses this by synthesizing missing sinogram data with a deep neural network.
- Sparse-view sampling uses fewer ray measurements with lower measured-data noise than tube-current reduction, but its clinical deployment remains unresolved.
- Sparse-view reconstruction is ill-posed, and iterative sparsity-based methods can produce parameter-dependent artifacts while requiring sufficient data for acceptable image quality.
- Applying filtered backprojection directly to sparse data causes poor-quality images with severe streak artifacts.
- Existing sinogram synthesis methods include linear, principal-component, partial-differential-equation, frequency-consistency, directional, dictionary-learning, and combinatorial approaches.
- The study implements a CNN-based method using reprojected real-patient CT data and compares it with CNN, analytic interpolation, and iterative reconstruction approaches.
II. METHODS
The method uses convolutional neural networks to learn task-relevant features without handcrafted feature definitions. In this application, the CNN performs supervised regression to synthesize missing sinogram data.
- A CNN combines convolution, pooling, fully connected, and activation layers to transform input data through learned representations.
- Convolutional layers apply learned weights and biases to input data, while pooling down-samples inputs using operations such as maximum or average pooling.
- Pooling generally promotes shift-invariant outputs, which is useful when target positions vary in segmentation or classification data.
- The network learns features during training, eliminating the need for handcrafted features as the cost function is minimized.
- Missing-sinogram synthesis is formulated as a regression problem for which CNN-based approaches have been successful.
B. Structure of the proposed network
The proposed network is a residual U-Net that replaces pooling with trainable convolutional down-sampling and combines input and final-layer outputs. It is trained by comparing predicted and ground-truth patches.
- The proposed architecture is a residual U-Net designed to learn differences between ground-truth and input sinogram data.
- Replacing pooling layers with convolutional layers allows the network to learn task-specific down-sampling weights.
- Down-sampling convolutional layers use stride 2, while the other convolutional layers use stride 1.
- At the bottom layer, the original input patch and the last convolution-layer output are summed within the residual-learning framework.
- The training cost function compares network output patches with corresponding ground-truth patches over batches.
C. Training the network
Training uses reprojections of real-patient lung CT images, quarter-rate angular sampling, linear interpolation for initial full sinograms, and overlapping patches for CNN input.
- Training and validation data were generated by reprojecting 7 real patients’ lung CT images from TCIA, using 634 slice images.
- Every fourth view was selected to create sparse sinograms with equal angular separation, then linear interpolation produced initial full sinograms for training.
- The training examples include original full sinograms, sparse-view sinograms, and linearly interpolated sinograms.
- The network uses 50×50 patches with stride 10; overlapping regions are averaged to mitigate tiling artifacts when forming the synthesized sinogram.
- The database contains 2,142,667 training patches and 918,285 validation patches, optimized with Adam.
D. Other methods for comparison
The study compares linear and directional sinogram interpolation with a 20-successive-convolution-layer CNN for synthesizing missing sparse-view data.
- Comparison methods: Linear interpolation fills missing sinogram data along the angular direction.Directional interpolation instead estimates object direction from sinogram gradients and uses Eigenvalue- and eigenvector-based interpolation weights.
- Comparison methods: The comparison includes a CNN composed of 20 successive convolutional layers.
E. Image reconstruction
The evaluation reconstructs images with filtered backprojection from ground-truth, sparse, interpolated, and CNN-synthesized sinograms, and also includes an iterative POCS-TV method.
- Reconstruction methods: Filtered backprojection reconstructs images from the ground-truth and synthesized sinograms for each imaging task.The tested FBP cases include sparse-view data, linear and directional interpolation, and two deep-neural-network syntheses.
- Reconstruction methods: POCS-TV provides an iterative reconstruction baseline that directly reconstructs images from sparsely sampled sinograms.It minimizes total variation using projection on convex sets.
A. Network training result
Both networks have similar validation and training Euclidean losses, while the U-Net achieves a smaller error than the successive convolutional-layer network.
- Training and validation loss: The U-Net produces a smaller Euclidean loss than the successive convolutional-layer network.Validation loss remains similar to training loss for both networks.
B. Interpolation results
Evaluation on held-out patient data shows that CNN-based sinogram synthesis improves sinogram and reconstructed-image quality, with U-Net performing best among the tested methods.
- Evaluation setup: 662 slices from 8 patients excluded from training and validation were used for objective evaluation.Evaluation sinograms followed the training CT geometry and were divided into training-sized patches.
- Quantitative measures: Sinogram comparisons use NRMSE, PSNR, and SSIM as quantitative image-quality measures.NRMSE is RMSE divided by the ground-truth image's maximum-minus-minimum value.
- Reconstructed-image results: NRMSE, PSNR, and SSIM were best for U-Net reconstructed images among all tested methods.The quantitative reconstructed-image comparisons are summarized in Tables VI to VIII.
- Reconstructed-image results: Direct FBP from sparse-view data produces severe streak artifacts, while TV minimization produces cartoon artifacts and can miss small structures.
- Reconstructed-image results: Linear and directional interpolation leave moderate streak artifacts, whereas CNN synthesis reduces them and U-Net leaves the fewest.
IV. DISCUSSION
The CNN-based sinogram synthesis produced reconstructed images comparable to those from fully sampled sinograms, while iterative reconstruction remained sensitive to cost functions and parameters. Training was computationally lengthy, although synthesis was much faster after training.
- CNN-based synthesis effectively filled missing sparse-view sinogram data and produced images comparable to fully sampled reconstructions.
- POCS-TV reconstructions were rather poor in this study, but fine-tuned iterative algorithms might achieve acceptable quality for a given imaging task.
- Compressed-sensing-inspired iterative methods may produce cartoon artifacts and miss small structures in sparse-view reconstructions.
- Training required about 5 days for successive convolutional layers and 12 days for the U-Net, whereas post-training synthesis took less than 10 seconds and 50 seconds, respectively.
- High training-data redundancy increased training time, motivating future investigation of redundancy reduction without compromising network performance.
V. CONCLUSION
The study developed a U-Net for sparse-view sinogram interpolation followed by FBP reconstruction and compared it with interpolation, CNN, and TV-minimization approaches. The proposed network produced promising results and may serve as an option for low-dose CT imaging.
- The study developed a U-Net to interpolate sparsely sampled sinograms for CT reconstruction using FBP.
- The proposed method was compared with linear, directional, and other-CNN sinogram interpolation methods, plus TV-minimization reconstruction from sparse data.
- Reconstructed images were compared across the proposed method and the other interpolation and reconstruction approaches.
- The proposed network produced promising results and is believed to be an option for low-dose CT imaging.