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Differentiable Forward Projector for X-ray Computed Tomography (2307.05801v1)

Published 11 Jul 2023 in cs.LG, cs.CV, and cs.MS

Abstract: Data-driven deep learning has been successfully applied to various computed tomographic reconstruction problems. The deep inference models may outperform existing analytical and iterative algorithms, especially in ill-posed CT reconstruction. However, those methods often predict images that do not agree with the measured projection data. This paper presents an accurate differentiable forward and back projection software library to ensure the consistency between the predicted images and the original measurements. The software library efficiently supports various projection geometry types while minimizing the GPU memory footprint requirement, which facilitates seamless integration with existing deep learning training and inference pipelines. The proposed software is available as open source: https://github.com/LLNL/LEAP.

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Citations (5)
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Summary

  • The paper presents LEAP, a differentiable forward/back projector that addresses data consistency issues in deep learning-based XCT reconstructions.
  • It leverages the Separable Footprint model and PyTorch integration to maintain high numerical fidelity and enable efficient GPU usage.
  • Experimental results on limited-angle CT data show marked improvements in PSNR and SSIM, validating LEAP’s impact on hybrid reconstruction pipelines.

An Expert Analysis of "Differentiable Forward Projector for X-ray Computed Tomography"

The paper "Differentiable Forward Projector for X-ray Computed Tomography" explores the intersection of deep learning (DL) and X-ray Computed Tomography (XCT), presenting a novel differentiable software library aimed at improving the consistency and accuracy of XCT image reconstructions. This work highlights the current challenges in applying DL to ill-posed inverse problems typical in limited-angle or sparse-view CT applications and provides a robust solution through an open-source tool that integrates seamlessly into existing DL frameworks.

Computational Challenges in XCT

The reconstruction of XCT data is a classic inverse problem, traditionally addressed by analytical methods like the Filtered Backprojection (FBP) or iterative reconstruction algorithms. These approaches, however, fall short in situations with incomplete data, such as limited-angle or few-view scenarios, where DL models have shown potential improvements. Despite these advancements, DL-based methods often suffer from a lack of data agreement, predicting images that deviate from the measured X-ray projection data, thus necessitating a data consistency mechanism.

Differentiable Forward and Back Projection Library

The paper introduces LivermorE AI Projector (LEAP), a differentiable forward and back projection library. This tool is designed to address the lack of data consistency by incorporating a precise forward model that enhances DL-based reconstruction pipelines. A key feature of LEAP is its minimal GPU memory footprint, enabling efficient integration with deep learning models without necessitating large memory allocations.

The LEAP library supports three prevalent 3D scanner geometries, namely parallel-beam, cone-beam, and customizable geometry configurations. This flexibility ensures applicability across various XCT systems, overcoming limitations of prior solutions that either consumed excessive memory or required singular neural network training per configuration.

Methodological Contributions

The LEAP software is grounded on the Separable Footprint (SF) projector model, well-regarded for its accuracy in modeling the finite dimensions of voxels and detector pixels. The utilization of this model ensures that LEAP's projections maintain high numerical fidelity across varying voxel and detector sizes.

The integration of LEAP into the DL ecosystem is facilitated via its PyTorch interface, allowing for automatic differentiation and tensor operations, which are pivotal for training neural networks. The software also maintains quantitative accuracy with CT projection data and reconstruction volumes representing real-world units.

Experimental Validation

An experimental evaluation underlined the efficacy of incorporating data consistency steps facilitated by LEAP. Conducted on a limited-angle CT problem using a publicly accessible dataset, the inclusion of the LEAP library significantly improved reconstruction metrics like PSNR and SSIM by ensuring the forward projections derived from neural network outputs aligned well with the original projection data. This demonstrates that the LEAP library not only enhances DL inference outputs but also serves as a vital component in hybrid reconstruction pipelines.

Implications and Future Directions

The development of a differentiable projector opens up new avenues in improving DL-based solutions for ill-posed inverse problems beyond XCT. It provides a systemic way to ensure data consistency, potentially impacting other imaging modalities and various fields where inverse problems are prevalent.

As research progresses, future work may explore extending LEAP's geometry support to fan-beam and helical cone-beam systems, broadening the range of compatible imaging configurations. Additionally, the exploration of stochastic gradient-based optimization techniques leveraging LEAP's differentiability could further scale the application to broader DL tasks, enhancing the precision and robustness of AI-driven reconstructions.

By providing an open-source platform, the authors have laid a foundation that could catalyze further innovations in CT reconstruction and beyond, fostering a community-driven approach to enhancing imaging science with artificial intelligence.

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