Tobías I. Liaudat

Selected publications

2026

1. 

   Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements

   Tom Sprunck, Marcelo Pereyra, and Tobias Liaudat

   Proceedings of the 43rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026., Jul 2026

   Abs arXiv Bib Code

   Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is unavailable, with a focus on model selection and misspecification diagnosis. Existing unsupervised model evaluation methods are often unsuitable for computational imaging due to their high computational cost and incompatibility with modern image priors defined implicitly via machine learning models. We herein propose a general methodology for unsupervised model selection and misspecification detection in Bayesian imaging sciences, based on a novel combination of Bayesian cross-validation and data fission, a randomized measurement splitting technique. The approach is compatible with any Bayesian imaging sampler, including diffusion and plug-and-play samplers. We demonstrate the methodology through experiments involving various scoring rules and types of model misspecification, where we achieve excellent selection and detection accuracy with a low computational cost.

   @article{sprunck2025,
     title = {Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements},
     author = {Sprunck, Tom and Pereyra, Marcelo and Liaudat, Tobias},
     year = {2026},
     journal = {Proceedings of the 43rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026.},
     eprint = {2510.27663},
     month = jul,
     archiveprefix = {arXiv},
     primaryclass = {eess.IV},
     url = {https://arxiv.org/abs/2510.27663}
   }

2024

1. 

   Scalable Bayesian uncertainty quantification with data-driven priors for radio interferometric imaging

   Tobías I. Liaudat, Matthijs Mars, Matthew A. Price, and 3 more authors

   RAS Techniques and Instruments, Aug 2024

   Abs arXiv DOI Bib Code

   Next-generation radio interferometers like the Square Kilometer Array have the potential to unlock scientific discoveries thanks to their unprecedented angular resolution and sensitivity. One key to unlocking their potential resides in handling the deluge and complexity of incoming data. This challenge requires building radio interferometric (RI) imaging methods that can cope with the massive data sizes and provide high-quality image reconstructions with uncertainty quantification (UQ). This work proposes a method coined quantifAI to address UQ in RI imaging with data-driven (learned) priors for high-dimensional settings. Our model, rooted in the Bayesian framework, uses a physically motivated model for the likelihood. The model exploits a data-driven convex prior potential, which can encode complex information learned implicitly from simulations and guarantee the log-concavity of the posterior. We leverage probability concentration phenomena of high-dimensional log-concave posteriors to obtain information about the posterior, avoiding MCMC sampling techniques. We rely on convex optimization methods to compute the MAP estimation, which is known to be faster and better scale with dimension than MCMC strategies. quantifAI allows us to compute local credible intervals and perform hypothesis testing of structure on the reconstructed image. We propose a novel fast method to compute pixel-wise uncertainties at different scales, which uses three and six orders of magnitude less likelihood evaluations than other UQ methods like length of the credible intervals and Monte Carlo posterior sampling, respectively. We demonstrate our method by reconstructing RI images in a simulated setting and carrying out fast and scalable UQ, which we validate with MCMC sampling. Our method shows an improved image quality and more meaningful uncertainties than the benchmark method based on a sparsity-promoting prior.

   @article{liaudat2023_3,
     author = {{Liaudat}, Tobías I. and {Mars}, Matthijs and {Price}, Matthew A. and {Pereyra}, Marcelo and {Betcke}, Marta M. and {McEwen}, Jason D.},
     title = {{Scalable Bayesian uncertainty quantification with data-driven priors for radio interferometric imaging}},
     journal = {RAS Techniques and Instruments},
     volume = {3},
     number = {1},
     pages = {505-534},
     year = {2024},
     month = aug,
     issn = {2752-8200},
     url = {https://doi.org/10.1093/rasti/rzae030},
     eprint = {https://academic.oup.com/rasti/article-pdf/3/1/505/59024060/rzae030.pdf}
   }

2023

1. 

   Rethinking data-driven point spread function modeling with a differentiable optical model

   Tobias Liaudat, Jean-Luc Starck, Martin Kilbinger, and 1 more author

   Inverse Problems, Feb 2023

   Abs arXiv DOI Bib Code

   In astronomy, upcoming space telescopes with wide-field optical instruments have a spatially varying point spread function (PSF). Specific scientific goals require a high-fidelity estimation of the PSF at target positions where no direct measurement of the PSF is provided. Even though observations of the PSF are available at some positions of the field of view (FOV), they are undersampled, noisy, and integrated into wavelength in the instrument’s passband. PSF modeling represents a challenging ill-posed problem, as it requires building a model from these observations that can infer a super-resolved PSF at any wavelength and position in the FOV. Current data-driven PSF models can tackle spatial variations and super-resolution. However, they are not capable of capturing PSF chromatic variations. Our model, coined WaveDiff, proposes a paradigm shift in the data-driven modeling of the point spread function field of telescopes. We change the data-driven modeling space from the pixels to the wavefront by adding a differentiable optical forward model into the modeling framework. This change allows the transfer of a great deal of complexity from the instrumental response into the forward model. The proposed model relies on efficient automatic differentiation technology and modern stochastic first-order optimization techniques recently developed by the thriving machine-learning community. Our framework paves the way to building powerful, physically motivated models that do not require special calibration data. This paper demonstrates the WaveDiff model in a simplified setting of a space telescope. The proposed framework represents a performance breakthrough with respect to the existing state-of-the-art data-driven approach. The pixel reconstruction errors decrease six-fold at observation resolution and 44-fold for a 3x super-resolution. The ellipticity errors are reduced at least 20 times, and the size error is reduced more than 250 times. By only using noisy broad-band in-focus observations, we successfully capture the PSF chromatic variations due to diffraction. WaveDiff source code and examples associated with this paper are available at this link.

   @article{liaudat2023,
     author = {Liaudat, Tobias and Starck, Jean-Luc and Kilbinger, Martin and Frugier, Pierre-Antoine},
     date-added = {2023-10-06 15:09:53 +0100},
     date-modified = {2023-10-06 15:09:53 +0100},
     journal = {Inverse Problems},
     month = feb,
     number = {3},
     pages = {035008},
     publisher = {IOP Publishing},
     title = {Rethinking data-driven point spread function modeling with a differentiable optical model},
     url = {https://dx.doi.org/10.1088/1361-6420/acb664},
     volume = {39},
     year = {2023},
     bdsk-url-1 = {https://dx.doi.org/10.1088/1361-6420/acb664}
   }