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Learned Primal-dual Reconstruction

arXiv 1707.06474 ↗First posted 20 Jul 2017math.OC cs.CV cs.NEcited by 251

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Abstract (arXiv)

We propose the Learned Primal-Dual algorithm for tomographic reconstruction. The algorithm accounts for a (possibly non-linear) forward operator in a deep neural network by unrolling a proximal primal-dual optimization method, but where the proximal operators have been replaced with convolutional neural networks. The algorithm is trained end-to-end, working directly from raw measured data and it does not depend on any initial reconstruction such as FBP. We compare performance of the proposed method on low dose CT reconstruction against FBP, TV, and deep learning based post-processing of FBP. For the Shepp-Logan phantom we obtain >6dB PSNR improvement against all compared methods. For human phantoms the corresponding improvement is 6.6dB over TV and 2.2dB over learned post-processing along with a substantial improvement in the SSIM. Finally, our algorithm involves only ten forward-back-projection computations, making the method feasible for time critical clinical applications.

Key facts. Cited by 251 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Jul 2017.

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Citing papers per year: 2021: 45; 2022: 51; 2023: 49; 2024: 38; 2025: 25; 2026: 43.

251 papers.

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  1. 2021Learning to Optimize: A Primer and A Benchmarkcited by 206
  2. 2021Deep Equilibrium Architectures for Inverse Problems in Imagingcited by 126
  3. 2022Adaptive Diffusion Priors for Accelerated MRI Reconstructioncited by 117
  4. 2022NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstructioncited by 106
  5. 2021Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformerscited by 76
  6. 2022DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstructioncited by 73
  7. 2024R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstructioncited by 65
  8. 2023ReFit: Recurrent Fitting Network for 3D Human Recoverycited by 47
  9. 2022Learned reconstruction methods with convergence guaranteescited by 46
  10. 2021Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detectioncited by 34
  11. 2021Recurrent Variational Network: A Deep Learning Inverse Problem Solver applied to the task of Accelerated MRI Reconstructioncited by 34
  12. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
38 more
  1. 2021End-to-end reconstruction meets data-driven regularization for inverse problemscited by 32
  2. 2021Equivariant neural networks for inverse problemscited by 29
  3. 2021Learning the optimal Tikhonov regularizer for inverse problemscited by 26
  4. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  5. 2021Regularising Inverse Problems with Generative Machine Learning Modelscited by 22
  6. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  7. 2022Online Deep Equilibrium Learning for Regularization by Denoisingcited by 22
  8. 2023Score-Based Generative Models for PET Image Reconstructioncited by 22
  9. 2024Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problemscited by 21
  10. 2021Learning Regularization Parameters of Inverse Problems via Deep Neural Networkscited by 19
  11. 2022UncertaINR: Uncertainty Quantification of End-to-End Implicit Neural Representations for Computed Tomographycited by 19
  12. 2021SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guaranteescited by 18
  13. 2021Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Futurecited by 18
  14. 2021Feasibility-based Fixed Point Networkscited by 17
  15. 2023Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restorationcited by 17
  16. 2024DPER: Diffusion Prior Driven Neural Representation for Limited Angle and Sparse View CT Reconstructioncited by 17
  17. 2024A study of why we need to reassess full reference image quality assessment with medical imagescited by 16
  18. 2023Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstructioncited by 15
  19. 2022Physics-/Model-Based and Data-Driven Methods for Low-Dose Computed Tomography: A surveycited by 14
  20. 2022Near-Exact Recovery for Tomographic Inverse Problems via Deep Learningcited by 13
  21. 2023Towards Constituting Mathematical Structures for Learning to Optimizecited by 13
  22. 2023Convergent regularization in inverse problems and linear plug-and-play denoiserscited by 13
  23. 2021Fourier Image Transformercited by 12
  24. 2021MetaPose: Fast 3D Pose from Multiple Views without 3D Supervisioncited by 12
  25. 2021DuDoTrans: Dual-Domain Transformer Provides More Attention for Sinogram Restoration in Sparse-View CT Reconstructioncited by 12
  26. 2022RIAV-MVS: Recurrent-Indexing an Asymmetric Volume for Multi-View Stereocited by 12
  27. 2024Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisationcited by 12
  28. 2025Learning Regularization Functionals for Inverse Problems: A Comparative Studycited by 12
  29. 2021A Geometry-Informed Deep Learning Framework for Ultra-Sparse 3D Tomographic Image Reconstructioncited by 11
  30. 2022NeAT: Neural Adaptive Tomographycited by 11
  31. 2022The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distributioncited by 11
  32. 2021An Optimal Control Framework for Joint-channel Parallel MRI Reconstruction without Coil Sensitivitiescited by 10
  33. 2022Uncertainty Quantification for Deep Unrolling-Based Computational Imagingcited by 10
  34. 2022Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priorscited by 9
  35. 2022Computed Tomography Reconstruction using Generative Energy-Based Priorscited by 9
  36. 2023PtychoDV: Vision Transformer-Based Deep Unrolling Network for Ptychographic Image Reconstructioncited by 9
  37. 2021Improving Generalizability in Limited-Angle CT Reconstruction with Sinogram Extrapolationcited by 8
  38. 2022Unrolled Primal-Dual Networks for Lensless Camerascited by 8

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