Generative Models for Poisson Inverse Problems: Application to Emission Imaging

Emission imaging relies on the detection of photons produced by radioactive decays. The main modalities are Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT). Due to the acquisition process, the measured data are sinograms corrupted by Poisson noise. Image reconstruction is therefore formulated as an ill-posed linear inverse problem.

Classical reconstruction methods such as the Maximum Likelihood Expectation Maximization (MLEM) algorithm are widely used in clinical systems but tend to amplify noise. Recent advances in deep learning and generative models, such as diffusion models and flow matching, provide powerful priors for inverse problems. However, their application to Poisson inverse problems in medical imaging remains limited and raises important reliability issues.

The objective is to integrate modern generative models into the reconstruction process for emission imaging, with a focus on Poisson noise modeling and algorithmic convergence.

More details

See document attached for more details

References

  1. L. A. Shepp and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Transactions on Medical Imaging, vol. 1, no. 2, pp. 113–122, 1982.
  2. K. Zhang, Y. Li, W. Zuo, L. Zhang, L. Van Gool, and R. Timofte, “Plug-and-Play Image Restoration With Deep Denoiser Prior,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, pp. 6360–6376, Oct. 2022.
  3. Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, “Score-based generative modeling through stochastic differential equations,” in ICLR, 2021.
  4. Y. Lipman, R. T. Q. Chen, H. Ben-Hamu, M. Nickel, and M. Le, “Flow Matching for Generative Modeling,” Feb. 2023, arXiv:2210.02747.
  5. H. Chung, J. Kim, M. T. McCann, M. L. Klasky, and J. C. Ye, “Diffusion posterior sampling for general noisy inverse problems,” in ICLR, 2023.
  6. G. Webber, Y. Mizuno, O. D. Howes, A. Hammers, A. P. King, and A. J. Reader, “Likelihood-Scheduled Score-Based Generative Modeling for Fully 3D PET Image Reconstruction,” IEEE Transactions on Medical Imaging, 2025.
  7. T. Modrzyk, A. Etxebeste, E. Bretin, and V. Maxim, “A convergent Plug-and-Play Majorization-Minimization algorithm for Poisson inverse problems,” 2025.