Tobías I. Liaudat

Selected publications

2023

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

   arXiv e-prints, Nov 2023

   Abs arXiv 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 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 radio-interferometric 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, 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 that let us obtain information about the posterior, avoiding MCMC sampling techniques. We rely on convex optimisation methods to compute the MAP estimation, which is known to be faster and better scale with dimension than MCMC sampling strategies. Our method allows us to compute local credible intervals, i.e., Bayesian error bars, and perform hypothesis testing of structure on the reconstructed image. In addition, we propose a novel blazing-fast method to compute pixel-wise uncertainties at different scales. We demonstrate our method by reconstructing radio-interferometric 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 = {arXiv e-prints},
     keywords = {Astrophysics - Instrumentation and Methods for Astrophysics, Computer Science - Machine Learning},
     year = {2023},
     month = nov,
     eid = {arXiv:2312.00125},
     pages = {arXiv:2312.00125},
     archiveprefix = {arXiv},
     eprint = {2312.00125},
     primaryclass = {astro-ph.IM},
     adsurl = {https://ui.adsabs.harvard.edu/abs/2023arXiv231200125L},
     adsnote = {Provided by the SAO/NASA Astrophysics Data System}
   }

2. 

   Proximal nested sampling with data-driven priors for physical scientists

   Jason D. McEwen, Tobías I. Liaudat, Matthew A. Price, and 2 more authors

   arXiv e-prints, Jun 2023

   Abs arXiv Bib Code

   Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging. The framework is suitable for models with a log-convex likelihood, which are ubiquitous in the imaging sciences. The purpose of this article is two-fold. First, we review proximal nested sampling in a pedagogical manner in an attempt to elucidate the framework for physical scientists. Second, we show how proximal nested sampling can be extended in an empirical Bayes setting to support data-driven priors, such as deep neural networks learned from training data.

   @article{mcewen2023,
     adsnote = {Provided by the SAO/NASA Astrophysics Data System},
     adsurl = {https://ui.adsabs.harvard.edu/abs/2023arXiv230700056M},
     archiveprefix = {arXiv},
     author = {{McEwen}, Jason D. and {Liaudat}, Tobías I. and {Price}, Matthew A. and {Cai}, Xiaohao and {Pereyra}, Marcelo},
     date-added = {2023-10-06 15:12:01 +0100},
     date-modified = {2023-10-06 15:12:15 +0100},
     doi = {10.48550/arXiv.2307.00056},
     eid = {arXiv:2307.00056},
     eprint = {2307.00056},
     journal = {arXiv e-prints},
     keywords = {Statistics - Methodology, Astrophysics - Instrumentation and Methods for Astrophysics, Statistics - Machine Learning},
     month = jun,
     pages = {arXiv:2307.00056},
     primaryclass = {stat.ME},
     title = {{Proximal nested sampling with data-driven priors for physical scientists}},
     year = {2023},
     bdsk-url-1 = {https://doi.org/10.48550/arXiv.2307.00056}
   }

3. 

   Point spread function modelling for astronomical telescopes: a review focused on weak gravitational lensing studies

   Tobias Liaudat, Jean-Luc Starck, and Martin Kilbinger

   Frontiers in Astronomy and Space Sciences, Jun 2023

   Abs arXiv Bib PDF

   The accurate modelling of the point spread function (PSF) is of paramount importance in astronomical observations, as it allows for the correction of distortions and blurring caused by the telescope and atmosphere. PSF modelling is crucial for accurately measuring celestial objects’ properties. The last decades have brought us a steady increase in the power and complexity of astronomical telescopes and instruments. Upcoming galaxy surveys like Euclid and Legacy Survey of Space and Time (LSST) will observe an unprecedented amount and quality of data. Modelling the PSF for these new facilities and surveys requires novel modelling techniques that can cope with the ever-tightening error requirements. The purpose of this review is threefold. Firstly, we introduce the optical background required for a more physically motivated PSF modelling and propose an observational model that can be reused for future developments. Secondly, we provide an overview of the different physical contributors of the PSF, which includes the optic- and detector-level contributors and atmosphere. We expect that the overview will help better understand the modelled effects. Thirdly, we discuss the different methods for PSF modelling from the parametric and non-parametric families for ground- and space-based telescopes, with their advantages and limitations. Validation methods for PSF models are then addressed, with several metrics related to weak-lensing studies discussed in detail. Finally, we explore current challenges and future directions in PSF modelling for astronomical telescopes.

   @article{liaudat2023_2,
     archiveprefix = {arXiv},
     author = {{Liaudat}, Tobias and {Starck}, Jean-Luc and {Kilbinger}, Martin},
     journal = {Frontiers in Astronomy and Space Sciences},
     volume = {10},
     issn = {2296-987X},
     doi = {10.3389/fspas.2023.1158213},
     month = jun,
     pages = {arXiv:2306.07996},
     primaryclass = {astro-ph.IM},
     title = {{Point spread function modelling for astronomical telescopes: a review focused on weak gravitational lensing studies}},
     year = {2023},
     bdsk-url-1 = {https://doi.org/10.48550/arXiv.2306.07996}
   }

4. 

   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 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},
     doi = {10.1088/1361-6420/acb664},
     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}
   }