Differentiable Forward and Back-Projector for Rigid Motion Estimation in X-ray Imaging
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arXiv
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| Format: | Preprint |
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2025
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| author | Jiang, Xiao Wang, Xin Uneri, Ali Zbijewski, Wojciech B. Stayman, J. Webster |
| author_facet | Jiang, Xiao Wang, Xin Uneri, Ali Zbijewski, Wojciech B. Stayman, J. Webster |
| contents | Objective: In this work, we propose a framework for differentiable forward and back-projector that enables scalable, accurate, and memory-efficient gradient computation for rigid motion estimation tasks. Methods: Unlike existing approaches that rely on auto-differentiation or that are restricted to specific projector types, our method is based on a general analytical gradient formulation for forward/backprojection in the continuous domain. A key insight is that the gradients of both forward and back-projection can be expressed directly in terms of the forward and back-projection operations themselves, providing a unified gradient computation scheme across different projector types. Leveraging this analytical formulation, we develop a discretized implementation with an acceleration strategy that balances computational speed and memory usage. Results: Simulation studies illustrate the numerical accuracy and computational efficiency of the proposed algorithm. Experiments demonstrates the effectiveness of this approach for multiple X-ray imaging tasks we conducted. In 2D/3D registration, the proposed method achieves ~8x speedup over an existing differentiable forward projector while maintaining comparable accuracy. In motion-compensated analytical reconstruction and cone-beam CT geometry calibration, the proposed method enhances image sharpness and structural fidelity on real phantom data while showing significant efficiency advantages over existing gradient-free and gradient-based solutions. Conclusion: The proposed differentiable projectors enable effective and efficient gradient-based solutions for X-ray imaging tasks requiring rigid motion estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differentiable Forward and Back-Projector for Rigid Motion Estimation in X-ray Imaging Jiang, Xiao Wang, Xin Uneri, Ali Zbijewski, Wojciech B. Stayman, J. Webster Medical Physics Image and Video Processing Objective: In this work, we propose a framework for differentiable forward and back-projector that enables scalable, accurate, and memory-efficient gradient computation for rigid motion estimation tasks. Methods: Unlike existing approaches that rely on auto-differentiation or that are restricted to specific projector types, our method is based on a general analytical gradient formulation for forward/backprojection in the continuous domain. A key insight is that the gradients of both forward and back-projection can be expressed directly in terms of the forward and back-projection operations themselves, providing a unified gradient computation scheme across different projector types. Leveraging this analytical formulation, we develop a discretized implementation with an acceleration strategy that balances computational speed and memory usage. Results: Simulation studies illustrate the numerical accuracy and computational efficiency of the proposed algorithm. Experiments demonstrates the effectiveness of this approach for multiple X-ray imaging tasks we conducted. In 2D/3D registration, the proposed method achieves ~8x speedup over an existing differentiable forward projector while maintaining comparable accuracy. In motion-compensated analytical reconstruction and cone-beam CT geometry calibration, the proposed method enhances image sharpness and structural fidelity on real phantom data while showing significant efficiency advantages over existing gradient-free and gradient-based solutions. Conclusion: The proposed differentiable projectors enable effective and efficient gradient-based solutions for X-ray imaging tasks requiring rigid motion estimation. |
| title | Differentiable Forward and Back-Projector for Rigid Motion Estimation in X-ray Imaging |
| topic | Medical Physics Image and Video Processing |
| url | https://arxiv.org/abs/2508.13304 |