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Deep Residual Learning for Compressed Sensing CT Reconstruction via Persistent Homology Analysis
Yo Seob Han, Jaejun Yoo, Jong Chul Ye
TL;DR
Sparse-view CT lowers radiation exposure but causes severe streaking artifacts, while iterative compressed-sensing reconstruction is computationally expensive. The paper uses persistent homology to motivate a residual network that estimates and subtracts artifacts, achieving improved reconstruction and much faster computation in experiments.
Problem
Sparse-view CT reconstruction must address severe streaking artifacts from insufficient projection views while avoiding the high computational cost of iterative compressed-sensing methods.
Method
The paper analyzes artifact and image manifolds with persistent homology and trains a residual architecture to estimate streaking artifacts for subtraction from sparse-view reconstructions.
Results
The proposed residual learning achieved significantly better reconstruction than conventional compressed-sensing CT while running extremely faster.
Takeaways & Limitations
Residual learning, especially the multi-scale U-net structure, is most effective for extremely sparse views because its enlarged receptive field captures globally distributed streaking artifacts.
Abstract
from arXiv · showhide
Recently, compressed sensing (CS) computed tomography (CT) using sparse projection views has been extensively investigated to reduce the potential risk of radiation to patient. However, due to the insufficient number of projection views, an analytic reconstruction approach results in severe streaking artifacts and CS-based iterative approach is computationally very expensive. To address this issue, here we propose a novel deep residual learning approach for sparse view CT reconstruction. Specifically, based on a novel persistent homology analysis showing that the manifold of streaking artifacts is topologically simpler than original ones, a deep residual learning architecture that estimates the streaking artifacts is developed. Once a streaking artifact image is estimated, an artifact-free image can be obtained by subtracting the streaking artifacts from the input image. Using extensive experiments with real patient data set, we confirm that the proposed residual learning provides significantly better image reconstruction performance with several orders of magnitude faster computational speed.
1. Introduction
Sparse-view CT reduces radiation exposure but creates severe streaking artifacts and makes iterative compressed-sensing reconstruction expensive. The paper proposes residual learning guided by persistent homology to estimate artifacts and reconstruct images efficiently.
- Motivation: Image reconstruction remains less investigated than diagnostic applications of deep learning in medical imaging.
- Motivation: Sparse-view CT reduces radiation dose by acquiring fewer projection views, but insufficient views cause severe streaking artifacts in FBP reconstructions.Compressed-sensing methods address these artifacts but require repeated projection and back-projection updates, making them computationally expensive.
- Proposed approach: The proposed residual network estimates streaking artifacts and subtracts them from the input to obtain an artifact-free image.The architecture targets reconstruction quality and computational speed without directly estimating high-texture CT images.
- Proposed approach: Persistent homology analysis indicates that the manifold of sparse-view streaking artifacts is topologically simpler than the original image manifold.This analysis motivates learning the residual artifacts rather than the artifact-free images directly.
- Architecture: Residual learning consistently outperforms image learning, while a multi-scale U-net architecture is most effective for removing artifacts from very sparse views.The paper attributes this advantage to enlarged receptive fields that capture globally distributed artifact patterns.
2. Related works
Prior CT deep-learning work primarily addressed low-dose noise, while sparse-view streaking artifacts remained difficult because their patterns are global. The paper positions its residual U-net approach as a new architecture for this reconstruction setting.
- Deep learning for CT: Deep-learning CT research included directional-wavelet CNNs for removing noise caused by reduced X-ray tube currents.
- Sparse-view artifacts: Sparse projection views produce globalized streaking patterns that conventional denoising CNNs struggle to remove.
- Residual learning: Residual learning had been applied to recognition, super-resolution, and denoising before this paper's sparse-view CT application.
- Architecture: The proposed U-net-derived architecture adds contracting paths and pooling or unpooling layers, with no prior use identified beyond image segmentation.
3. Theoretical backgrounds
This section introduces learning-theoretic motivation, CT reconstruction fundamentals, and persistent homology as a tool for showing that streaking-artifact manifolds are topologically simpler than original image manifolds.
- Generalization bound: Learning methods balance empirical data fidelity against a network-dependent complexity term to reduce generalization risk.The framework motivates controlling both empirical risk and model complexity.
- CT reconstruction background: Sparse projection views reduce radiation dose but cause severe streaking artifacts in standard filtered back-projection, while compressed-sensing reconstruction is computationally expensive.Insufficient projection views create artifacts radiating from targets and across reconstructions.
- Persistent homology: Persistent homology analyzes manifold complexity by tracking Betti numbers as the allowable point-cloud distance ϵ increases.Betti numbers count connected components and cycles, while barcode persistence captures how long topological features remain.
- Persistent homology: The paper applies persistent homology to label manifolds, focusing on residual streaking artifacts rather than network-input topology.This differs from prior work using Betti numbers as a neural-network capacity measure.
- Network design: An enlarged effective receptive field is advantageous for removing streaking artifacts because their patterns are globally distributed.The comparison concerns a multi-scale architecture versus a reference network without pooling.
4. Residual Learning Architecture
The proposed residual network uses convolutional processing with batch normalization, ReLU activations, and U-net-style contracting-path concatenations. Its multi-scale design enlarges the effective receptive field, benefiting removal of globally distributed streaking artifacts.
- Each network stage uses sequential 3 × 3 convolution, batch normalization, and ReLU layers, while the final stage ends with a 1 × 1 convolution.The network also includes a contracting path with concatenation.
- Pooling layers double the number of channels, and scale-by-scale contracting paths concatenate earlier features with later representations.
- The proposed multi-scale architecture enlarges the effective receptive field compared with a reference network without pooling.This enlarged field is advantageous for removing globally distributed streaking artifacts.
5. Experimental Results
Experiments used sparse-view reconstructions from patient CT data and compared the proposed method with TV-based compressed sensing reconstruction. The proposed method removed most streaking patterns, preserved detail, and reconstructed slices much faster.
- Data Set: Training used nine patient datasets with full-view 2304-view FBP references and sparse-view inputs from 48, 64, 96, and 192 projections.Eight patients were used for training and one for testing.
- Persistent Homology Analysis: Persistent-homology analysis showed that the residual-image manifold is topologically simpler than the original-image manifold.The comparison used Betti-number changes computed from point clouds of 512 × 512 label images.
- Reconstruction Results: The proposed reconstruction produced accurate coronal and sagittal images, while TV reconstruction retained patterned artifacts.
- Reconstruction Results: 123ms/slice was the proposed method's computational time, compared with about 3 ∼4 sec/slice for the TV approach.The paper reports significantly improved reconstruction results alongside this speed difference.
- Reconstruction Results: The network removed most streaking patterns while preserving detailed underlying structures across reconstructions from 48, 64, and 96 projection views.The same network was used for these cases.
6. Discussion
Comparative studies found residual learning superior to direct image learning and multi-scale residual learning superior to single-scale designs, especially for extremely sparse views. Training across 48 and 96 views improved robustness across view down-sampling ranges.
- Residual Learning vs. Image Learning: Residual learning converged faster and achieved better final performance than image learning.Magnified reconstructions showed that residual learning recovered internal-organ detail that image learning did not fully recover.
- Single-scale vs. Multi-scale Residual Learning: Multi-scale residual learning converged faster and produced better reconstruction quality than single-scale residual learning.The comparison controlled network parameters by using similar parameter counts.
- Single-scale vs. Multi-scale Residual Learning: In extremely sparse projection views, multi-scale structures consistently outperformed single-scale residual learning according to PSNR.At 192 views, single-scale residual learning began to outperform multi-scale image-learning approaches as global artifacts became less dominant.
- Diversity of Training Set: A network trained with 96-view data preserved detail best on denser inputs but could not reconstruct 48-view sparse CT without remaining streaking artifacts.
- Diversity of Training Set: Combining 48- and 96-view training data provided the best reconstruction across wide ranges of view down-sampling.
7. Conclusion
The paper concludes that persistent-homology analysis supports learning streaking-artifact residuals because their manifold is simpler than the original image manifold. Its multi-scale U-net residual network was most effective for very sparse views and substantially faster than conventional compressed sensing CT.
- Conclusion: Persistent-homology analysis and experiments supported the claim that the streaking-artifact residual manifold is topologically simpler than the original manifold.
- Conclusion: The multi-scale residual network using a U-net structure was most effective when the number of projection views was extremely small.The paper attributes this effectiveness to U-net's enlarged receptive field for globally distributed streaking artifacts.
- Conclusion: Extensive experiments found the proposed deep residual learning significantly better than conventional compressed sensing CT approaches.
- Conclusion: The proposed approach was extremely faster computationally than compressed sensing CT.
- Conclusion: Although developed for sparse-view CT reconstruction, the residual network may also be used to remove globally distributed image noise and artifacts.