arXiv subjects

Tobías I. Liaudat

Publications and source records attributed to Tobías I. Liaudat.

11 recordsLinked to original sources

arXiv2026

RPCA: a Resolved PSF reconstruction method for undersampled images

The Point-Spread Function (PSF) is a critical component in various astrophysical research areas, including galaxy morphology, photometric redshift determination, and weak lensing studies. As the next generation of space telescopes prepares for operations, including the China Space Station Telescope (CSST), accurate PSF modeling has become increasingly important. However, accurately modeling the PSF remains challenging, particularly for poorly sampled images. To construct reliable PSF models based on star images, we aim to develop a novel and robust method, which accounts for the pixel integration effect in modeling for reconstructing high-resolution PSFs from undersampled or poorly resolved images. In this paper, we present Resolved Principal Components Analysis (RPCA), a novel approach that accounts for pixel integration effects to enable the direct reconstruction of resolved PSFs from undersampled images via an Expectation-Maximization PCA (EMPCA) technique. Our method has been tested on a simulated PSF dataset for the China Space Station Telescope (CSST), where both observational and detector-induced effects were considered during simulation. The results demonstrate that RPCA achieves superior precision in PSF shape parameters compared to existing methods such as Multi-CCD (MCCD), Resolved Components Analysis (RCA), and PSFEx. Notably, RPCA {could reduce the bias of $ΔR^2/R^2$ by approximately one order of magnitude with respect to MCCD, RCA and PSFEx. RPCA exhibits robust stability under realistic observational conditions, including varying signal-to-noise ratios (SNRs) and contamination from cosmic rays and bad pixels. This suggests that RPCA could be a promising candidate for future CSST PSF modeling efforts.

astro-ph.IM↗

arXiv2026

Self-Supervised Conformal Prediction with Equivariant Bootstrapping for Image Uncertainty Quantification

Inverse problems are ubiquitous in modern scientific studies and involve recovering an underlying signal from noisy observations often transformed by a measurement operator. These problems are frequently ill-posed, particularly in imaging, leading to multiple plausible solutions and considerable uncertainty in reconstructed images. In fields like the physical and biological sciences, accurate uncertainty quantification (UQ) is critical for trustworthy scientific analyses and confident diagnoses. Current UQ methods for imaging often fall short; they can be inaccurate, or require unavailable or difficult-to-acquire ground truth data for calibration, which can introduce hidden biases due to distribution shifts between calibration and observed data. We introduce a UQ approach that leverages equivariant bootstrapping to generate heuristic coverages by exploiting data symmetries. We then refine these coverages through a conformal prediction calibration step, while crucially employing a self-supervised approach to avoid the need for ground truth calibration data. We demonstrate this method with weak lensing mass-mapping, where we aim to reconstruct the convergence field from shear measurements of distant galaxies weakly-lensed by gravitational fields. Mass-mapping in particular benefits from the self-supervised approach, as simulating calibration data is expensive and relies on specific cosmological models that could introduce biases in downstream cosmological inference tasks.

stat.ME↗

arXiv2026

Deep unfolding of MCMC kernels: scalable, modular & explainable GANs for high-dimensional posterior sampling

Markov chain Monte Carlo (MCMC) methods are fundamental to Bayesian computation, but can be computationally intensive, especially in high-dimensional settings. Push-forward generative models, such as generative adversarial networks (GANs), variational auto-encoders and normalising flows offer a computationally efficient alternative for posterior sampling. However, push-forward models are opaque as they lack the modularity of Bayes Theorem, leading to poor generalisation with respect to changes in the likelihood function. In this work, we introduce a novel approach to GAN architecture design by applying deep unfolding to Langevin MCMC algorithms. This paradigm maps fixed-step iterative algorithms onto modular neural networks, yielding architectures that are both flexible and amenable to interpretation. Crucially, our design allows key model parameters to be specified at inference time, offering robustness to changes in the likelihood parameters. We train these unfolded samplers end-to-end using a supervised regularized Wasserstein GAN framework for posterior sampling. Through extensive Bayesian imaging experiments, we demonstrate that our proposed approach achieves high sampling accuracy and excellent computational efficiency, while retaining the physics consistency, adaptability and interpretability of classical MCMC strategies.

cs.LG↗

arXiv2025

Generative modelling for mass-mapping with fast uncertainty quantification

Understanding the nature of dark matter in the Universe is an important goal of modern cosmology. A key method for probing this distribution is via weak gravitational lensing mass-mapping - a challenging ill-posed inverse problem where one infers the convergence field from observed shear measurements. Upcoming stage IV surveys, such as those made by the Vera C. Rubin Observatory and Euclid satellite, will provide a greater quantity and precision of data for lensing analyses, necessitating high-fidelity mass-mapping methods that are computationally efficient and that also provide uncertainties for integration into downstream cosmological analyses. In this work we introduce MMGAN, a novel mass-mapping method based on a regularised conditional generative adversarial network (GAN) framework, which generates approximate posterior samples of the convergence field given shear data. We adopt Wasserstein GANs to improve training stability and apply regularisation techniques to overcome mode collapse, issues that otherwise are particularly acute for conditional GANs. We train and validate our model on a mock COSMOS-style dataset before applying it to true COSMOS survey data. Our approach significantly outperforms the Kaiser-Squires technique and achieves similar reconstruction fidelity as alternative state-of-the-art deep learning approaches. Notably, while alternative approaches for generating samples from a learned posterior are slow (e.g. requiring $\sim$10 GPU minutes per posterior sample), MMGAN can produce a high-quality convergence sample in less than a second.

astro-ph.CO↗

arXiv2025

Generative imaging for radio interferometry with fast uncertainty quantification

With the rise of large radio interferometric telescopes, particularly the SKA, there is a growing demand for computationally efficient image reconstruction techniques. Existing reconstruction methods, such as the CLEAN algorithm or proximal optimisation approaches, are iterative in nature, necessitating a large amount of compute. These methods either provide no uncertainty quantification or require large computational overhead to do so. Learned reconstruction methods have shown promise in providing efficient and high quality reconstruction. In this article we explore the use of generative neural networks that enable efficient approximate sampling of the posterior distribution for high quality reconstructions with uncertainty quantification. Our RI-GAN framework, builds on the regularised conditional generative adversarial network (rcGAN) framework by integrating a gradient U-Net (GU-Net) architecture - a hybrid reconstruction model that embeds the measurement operator directly into the network. This framework uses Wasserstein GANs to improve training stability in combination with regularisation terms that combat mode collapse, which are typical problems for conditional GANs. This approach takes as input the dirty image and the point spread function (PSF) of the observation and provides efficient, high-quality image reconstructions that are robust to varying visibility coverages, generalises to images with an increased dynamic range, and provides informative uncertainty quantification. Our methods provide a significant step toward computationally efficient, scalable, and uncertainty-aware imaging for next-generation radio telescopes.

astro-ph.IM↗

arXiv2025

DeepInverse: A Python package for solving imaging inverse problems with deep learning

DeepInverse is an open-source PyTorch-based library for solving imaging inverse problems. The library covers all crucial steps in image reconstruction from the efficient implementation of forward operators (e.g., optics, MRI, tomography), to the definition and resolution of variational problems and the design and training of advanced neural network architectures. In this paper, we describe the main functionality of the library and discuss the main design choices.

eess.IV↗

arXiv2025

UNIONS: The Ultraviolet Near-Infrared Optical Northern Survey

The Ultraviolet Near-Infrared Optical Northern Survey (UNIONS) is a "collaboration of collaborations" that is using the Canada-France-Hawai'i Telescope, the Pan-STARRS telescopes, and the Subaru Observatory to obtain $ugriz$ images of a core survey region of 6250 deg$^2$ of the northern sky. The $10σ$ point source depth of the data, as measured within a 2-arcsecond diameter aperture, are $[u,g,r,i,z] = [23.7, 24.5, 24.2, 23.8, 23.3]$\ in AB magnitudes. UNIONS is addressing some of the most fundamental questions in astronomy, including the properties of dark matter, the growth of structure in the Universe from the very smallest galaxies to large-scale structure, and the assembly of the Milky Way. It is set to become the major ground-based legacy survey for the northern hemisphere for the next decade and provides an essential northern complement to the static-sky science of the Vera C. Rubin Observatory's Legacy Survey of Space and Time. UNIONS supports the core science mission of the {\it Euclid} space mission by providing the data necessary in the northern hemisphere for the calibration of the wavelength dependence of the {\it Euclid} point-spread function and derivation of photometric redshifts in the North Galactic Cap. This region contains the highest quality sky for {\it Euclid}, with low backgrounds from the zodiacal light, stellar density, extinction, and emission from Galactic cirrus. Here, we describe the UNIONS survey components, science goals, data products, and the current status of the overall program.

astro-ph.GA↗

arXiv2024

LoFi: Neural Local Fields for Scalable Image Reconstruction

Neural fields or implicit neural representations (INRs) have attracted significant attention in computer vision and imaging due to their efficient coordinate-based representation of images and 3D volumes. In this work, we introduce a coordinate-based framework for solving imaging inverse problems, termed LoFi (Local Field). Unlike conventional methods for image reconstruction, LoFi processes local information at each coordinate separately by multi-layer perceptrons (MLPs), recovering the object at that specific coordinate. Similar to INRs, LoFi can recover images at any continuous coordinate, enabling image reconstruction at multiple resolutions. With comparable or better performance than standard deep learning models like convolutional neural networks (CNNs) and vision transformers (ViTs), LoFi achieves excellent generalization to out-of-distribution data with memory usage almost independent of image resolution. Remarkably, training on 1024x1024 images requires less than 200MB of memory -- much below standard CNNs and ViTs. Additionally, LoFi's local design allows it to train on extremely small datasets with 10 samples or fewer, without overfitting and without the need for explicit regularization or early stopping.

cs.CV↗

arXiv2024

Uncertainty quantification for fast reconstruction methods using augmented equivariant bootstrap: Application to radio interferometry

The advent of next-generation radio interferometers like the Square Kilometer Array promises to revolutionise our radio astronomy observational capabilities. The unprecedented volume of data these devices generate requires fast and accurate image reconstruction algorithms to solve the ill-posed radio interferometric imaging problem. Most state-of-the-art reconstruction methods lack trustworthy and scalable uncertainty quantification, which is critical for the rigorous scientific interpretation of radio observations. We propose an unsupervised technique based on a conformalized version of a radio-augmented equivariant bootstrapping method, which allows us to quantify uncertainties for fast reconstruction methods. Noticeably, we rely on reconstructions from ultra-fast unrolled algorithms. The proposed method brings more reliable uncertainty estimations to our problem than existing alternatives.

astro-ph.IM↗

arXiv2024

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

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. QuantifAI's source code: https://github.com/astro-informatics/QuantifAI.

astro-ph.IM↗

arXiv2023

Proximal nested sampling with data-driven priors for physical scientists

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.

stat.ME↗