Constraint-Driven Imaging

Constraint-Driven Imaging

Modern X-ray imaging increasingly operates under constraints: limited angles, low signal, motion blur, or compressed acquisition geometries. These constraints arise from practical factors such as time-resolved acquisition, dose sensitivity, or hardware limits. Across different modalities our work addresses the same core challenge: how to recover meaningful structure when the data are insufficient on their own. 

The key lies in regularization: introducing well-chosen constraints that reflect physical, statistical, or structural expectations about the underlying signal. Regularization allows inverse problems to be solved even when data are noisy, incomplete, or highly undersampled. This principle runs through our efforts, from analytical MAP estimation to learned priors in generative models.

Statistical Regularization

Statistical regularization refers to the use of explicit, mathematically defined priors such as smoothness, sparsity, or continuity to stabilize inverse problems. These priors are embedded in optimization frameworks, typically through maximum a posteriori (MAP) estimation or penalized-likelihood methods. They allow reconstructions to remain meaningful when data are noisy, incomplete, or undersampled. In early and many current imaging pipelines, such priors are grounded in known physics or empirical assumptions and are often essential in scenarios where training data are unavailable or experimental constraints are severe. 

Our work applies these principles across different imaging modalities, using tailored regularization strategies that align with the structure of the underlying data:

  • Diffraction tomography uses smoothness-promoting MAP priors to reduce aliasing in crystallographic phase reconstructions.
  • X-ray fluorescence tomography incorporates spatio-spectral penalties to enhance elemental mapping under low photon counts
  • Time-resolved micro-tomography fuel spray imaging applies iterative solvers with temporal coherence constraints to reconstruct dynamic spray fields.
  • Nonrigid nano-tomography couples total variation with deformation models for dose-efficient, motion-aware reconstructions. 

These approaches establish a robust foundation for reconstruction by encoding known structure and constraints directly into the optimization problem. However, as data complexity grows and structural priors become harder to handcraft, a shift toward learned regularization has emerged, where constraints are not explicitly defined but instead learned from data.

Learned and Data-Driven Regularization

As imaging problems grow more complex and structural priors become harder to define explicitly, there has been a shift toward learned and data-driven regularization. These methods rely on neural networks (either trained or untrained) to model the structure of images or sinograms implicitly. Instead of specifying what a “good” solution looks like through equations, these approaches learn it from data, either during training or through the reconstruction process itself. 

This shift builds upon the foundations of statistical regularization but offers greater flexibility, particularly when working with sparse-view data, nonlinear forward models, or structures too complex to capture with simple priors. These learned approaches often integrate seamlessly into modular optimization frameworks, where they act as plug-in priors, denoisers, or sinogram predictors. 

In our work, we apply these principles across different imaging tasks: 

  • Deep image priors (DIPs) use the architecture of convolutional networks to regularize limited-angle CT without external training data.
  • Generative adversarial networks (GANs) complete sinograms in undersampled CT by learning geometric continuity from data.
  • Generative priors in ptycho-tomography are embedded in an ADMM-based solver to jointly reconstruct phase and structure under sparse and noisy conditions. 

These data-driven methods extend regularization beyond what hand-crafted models can provide. When integrated with physics-based solvers, they offer a hybrid path forward, balancing interpretability, flexibility, and reconstruction quality in the context of modern X-ray imaging systems.

Alignment with APS Upgrade

The APS Upgrade brings higher coherent flux, faster acquisition, and more complex experimental modes. Regularization (both statistical and learned) enables imaging workflows to adapt to these changes. 

  • Sparse and fast scanning: Regularization supports reconstruction from reduced projections, aligning with high-throughput and limited-angle acquisitions.
  • Low-dose and low-signal imaging: It stabilizes reconstructions in photon-limited conditions, critical for dose-sensitive samples.
  • Dynamic and in situ measurements: Time-aware and deformation-tolerant models recover evolving structures from minimal data.
  • Hybrid and high-dimensional imaging: Modular regularization frameworks handle diffraction, spectral, and phase data jointly. 

Regularization makes reconstruction feasible, reliable, and flexible, keeping pace with the expanded capabilities of APS-U.

References

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  • Gürsoy D, Biçer T, Lanzirotti A, Newville MG, De Carlo F. Hyperspectral image reconstruction for x-ray fluorescence tomography. Optics express. 2015 Apr 1;23(7):9014-23.
  • Duke DJ, Swantek AB, Sovis NM, Tilocco FZ, Powell CF, Kastengren AL, Gürsoy D, Biçer T. Time-resolved x-ray tomography of gasoline direct injection sprays. SAE International Journal of Engines. 2016 Apr 1;9(1):143-53.
  • Yang X, De Andrade V, Scullin W, Dyer EL, Kasthuri N, De Carlo F, Gürsoy D. Low-dose x-ray tomography through a deep convolutional neural network. Scientific reports. 2018 Feb 7;8(1):2575.
  • Liu Z, Bicer T, Kettimuthu R, Gursoy D, De Carlo F, Foster I. TomoGAN: low-dose synchrotron x-ray tomography with generative adversarial networks: discussion. Journal of the Optical Society of America A. 2020 Feb 12;37(3):422-34.
  • Barutcu S, Gürsoy D, Katsaggelos AK. Compressive ptychography using deep image and generative priors. arXiv preprint arXiv:2205.02397. 2022 May 5.
  • Barutcu S, Katsaggelos AK, Gürsoy D. A Deep Generative Approach to Oversampling in Ptychography. arXiv preprint arXiv:2207.14392. 2022 Jul 28.
  • Aslan S, Liu Z, Nikitin V, Bicer T, Leyffer S, Gürsoy D. Joint ptycho-tomography with deep generative priors. Machine Learning: Science and Technology. 2021 Aug 27;2(4):045017.
  • Barutcu S, Aslan S, Katsaggelos AK, Gürsoy D. Limited-angle computed tomography with deep image and physics priors. Scientific reports. 2021 Sep 6;11(1):17740.
  • Yoo S, Yang X, Wolfman M, Gursoy D, Katsaggelos AK. Sinogram image completion for limited angle tomography with generative adversarial networks. In2019 IEEE International Conference on Image Processing (ICIP) 2019 Sep 22 (pp. 1252-1256). IEEE.