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CT Reconstruction using Diffusion Posterior Sampling conditioned on a Nonlinear Measurement Model (2312.01464v2)

Published 3 Dec 2023 in physics.med-ph, cs.CV, eess.IV, and physics.comp-ph

Abstract: Diffusion models have been demonstrated as powerful deep learning tools for image generation in CT reconstruction and restoration. Recently, diffusion posterior sampling, where a score-based diffusion prior is combined with a likelihood model, has been used to produce high quality CT images given low-quality measurements. This technique is attractive since it permits a one-time, unsupervised training of a CT prior; which can then be incorporated with an arbitrary data model. However, current methods rely on a linear model of x-ray CT physics to reconstruct or restore images. While it is common to linearize the transmission tomography reconstruction problem, this is an approximation to the true and inherently nonlinear forward model. We propose a new method that solves the inverse problem of nonlinear CT image reconstruction via diffusion posterior sampling. We implement a traditional unconditional diffusion model by training a prior score function estimator, and apply Bayes rule to combine this prior with a measurement likelihood score function derived from the nonlinear physical model to arrive at a posterior score function that can be used to sample the reverse-time diffusion process. This plug-and-play method allows incorporation of a diffusion-based prior with generalized nonlinear CT image reconstruction into multiple CT system designs with different forward models, without the need for any additional training. We develop the algorithm that performs this reconstruction, including an ordered-subsets variant for accelerated processing and demonstrate the technique in both fully sampled low dose data and sparse-view geometries using a single unsupervised training of the prior.

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References (26)
  1. Kang, E., Min, J., and Ye, J. C., “A deep convolutional neural network using directional wavelets for low-dose x-ray ct reconstruction,” Medical physics 44(10), e360–e375 (2017).
  2. Wu, D., Kim, K., El Fakhri, G., and Li, Q., “Iterative low-dose ct reconstruction with priors trained by artificial neural network,” IEEE transactions on medical imaging 36(12), 2479–2486 (2017).
  3. Jing, J., Xia, W., Hou, M., Chen, H., Liu, Y., Zhou, J., and Zhang, Y., “Training low dose ct denoising network without high quality reference data,” Physics in Medicine & Biology 67(8), 084002 (2022).
  4. Kazerouni, A., Aghdam, E. K., Heidari, M., Azad, R., Fayyaz, M., Hacihaliloglu, I., and Merhof, D., “Diffusion models in medical imaging: A comprehensive survey,” Medical Image Analysis , 102846 (2023).
  5. Chung, H., Sim, B., Ryu, D., and Ye, J. C., “Improving diffusion models for inverse problems using manifold constraints,” Advances in Neural Information Processing Systems 35, 25683–25696 (2022).
  6. Müller-Franzes, G., Niehues, J. M., Khader, F., Arasteh, S. T., Haarburger, C., Kuhl, C., Wang, T., Han, T., Nebelung, S., Kather, J. N., et al., “Diffusion probabilistic models beat gans on medical images,” arXiv preprint arXiv:2212.07501 (2022).
  7. Liu, J., Anirudh, R., Thiagarajan, J. J., He, S., Mohan, K. A., Kamilov, U. S., and Kim, H., “Dolce: A model-based probabilistic diffusion framework for limited-angle ct reconstruction,” arXiv preprint arXiv:2211.12340 (2022).
  8. Xia, W., Cong, W., and Wang, G., “Patch-based denoising diffusion probabilistic model for sparse-view ct reconstruction,” arXiv preprint arXiv:2211.10388 (2022).
  9. Ho, J., Jain, A., and Abbeel, P., “Denoising diffusion probabilistic models,” Advances in neural information processing systems 33, 6840–6851 (2020).
  10. Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B., “Score-based generative modeling through stochastic differential equations,” arXiv preprint arXiv:2011.13456 (2020).
  11. Tivnan, M., Teneggi, J., Lee, T.-C., Zhang, R., Boedeker, K., Cai, L., Gang, G. J., Sulam, J., and Stayman, J. W., “Fourier diffusion models: A method to control mtf and nps in score-based stochastic image generation,” arXiv preprint arXiv:2303.13285 (2023).
  12. Song, Y., Shen, L., Xing, L., and Ermon, S., “Solving inverse problems in medical imaging with score-based generative models,” arXiv preprint arXiv:2111.08005 (2021).
  13. Chung, H., Kim, J., Mccann, M. T., Klasky, M. L., and Ye, J. C., “Diffusion posterior sampling for general noisy inverse problems,” arXiv preprint arXiv:2209.14687 (2022).
  14. Lopez Montes, A., McSkimming, T., Zbijewksi, W., Skeats, A., Delnooz, C., Siewerdsen, J., and Sisneiga, A., “Diffusion posterior sampling-based reconstruction for stationary ct imaging of intracranial hemorrhage,” in [Int’l Mtg. on Fully 3D Image Recon in Rad. & Nuc. Med. ], (2023).
  15. Bushe, D., Zhang, R., Chen, G.-H., and Li, K., “Unbiased zero-count correction method in low-dose high-resolution photon counting detector ct,” Physics in Medicine & Biology 68(11), 115002 (2023).
  16. Hsieh, J., Molthen, R. C., Dawson, C. A., and Johnson, R. H., “An iterative approach to the beam hardening correction in cone beam ct,” Medical physics 27(1), 23–29 (2000).
  17. Tilley, S., Siewerdsen, J. H., and Stayman, J. W., “Model-based iterative reconstruction for flat-panel cone-beam ct with focal spot blur, detector blur, and correlated noise,” Physics in Medicine & Biology 61(1), 296 (2015).
  18. Hyvärinen, A. and Dayan, P., “Estimation of non-normalized statistical models by score matching.,” Journal of Machine Learning Research 6(4) (2005).
  19. Tilley, S., Jacobson, M., Cao, Q., Brehler, M., Sisniega, A., Zbijewski, W., and Stayman, J. W., “Penalized-likelihood reconstruction with high-fidelity measurement models for high-resolution cone-beam imaging,” IEEE transactions on medical imaging 37(4), 988–999 (2017).
  20. Ronneberger, O., Fischer, P., and Brox, T., “U-net: Convolutional networks for biomedical image segmentation,” in [MICCAI 2015 ], 234–241, Springer (2015).
  21. Segars, W. P., Sturgeon, G., Mendonca, S., Grimes, J., and Tsui, B. M., “4d xcat phantom for multimodality imaging research,” Medical physics 37(9), 4902–4915 (2010).
  22. Xia, W., Shi, Y., Niu, C., Cong, W., and Wang, G., “Diffusion prior regularized iterative reconstruction for low-dose ct,” arXiv preprint arXiv:2310.06949 (2023).
  23. Erdogan, H. and Fessler, J. A., “Ordered subsets algorithms for transmission tomography,” Physics in Medicine & Biology 44(11), 2835 (1999).
  24. Ahn, S. and Fessler, J. A., “Globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms,” IEEE transactions on medical imaging 22(5), 613–626 (2003).
  25. Hudson, H. M. and Larkin, R. S., “Accelerated image reconstruction using ordered subsets of projection data,” IEEE transactions on medical imaging 13(4), 601–609 (1994).
  26. Kim, H. and Champley, K., “Differentiable forward projector for x-ray computed tomography,” arXiv preprint arXiv:2307.05801 (2023).
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