Alexandre Adam

Pablo Lemos

No'e Dia

Mircea Petrache

Ugo Niccolo Di Carlo

Alessandro A. Trani

2023-11-27

ArXiv (preprint)

arxiv.org

Score-Based Likelihood Characterization for Inverse Problems in the Presence of Non-Gaussian Noise

Ronan Legin

Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function… (see more) of complex, high-dimensional, non-Gaussian, and anisotropic noise. This work presents Score-based LIkelihood Characterization (SLIC), a framework that resolves this issue by building a data-driven noise model using a set of noise realizations from observations. We show that the approach produces unbiased and precise likelihoods even in the presence of highly non-Gaussian correlated and spatially varying noise. We use diffusion generative models to estimate the gradient of the probability density of noise with respect to data elements. In combination with the Jacobian of the physical model of the signal, we use Langevin sampling to produce independent samples from the unbiased likelihood. We demonstrate the effectiveness of the method using real data from the Hubble Space Telescope and James Webb Space Telescope.

2023-11-03

NeurIPS.cc/2023/Workshop/Deep_Inverse (poster)

openreview.net

Pixelated Reconstruction of Foreground Density and Background Surface Brightness in Gravitational Lensing Systems Using Recurrent Inference Machines

Max Welling

Modeling strong gravitational lenses in order to quantify distortions in the images of background sources and to reconstruct the mass densit… (see more)y in foreground lenses has been a difficult computational challenge. As the quality of gravitational lens images increases, the task of fully exploiting the information they contain becomes computationally and algorithmically more difficult. In this work, we use a neural network based on the recurrent inference machine to reconstruct simultaneously an undistorted image of the background source and the lens mass density distribution as pixelated maps. The method iteratively reconstructs the model parameters (the image of the source and a pixelated density map) by learning the process of optimizing the likelihood given the data using the physical model (a ray-tracing simulation), regularized by a prior implicitly learned by the neural network through its training data. When compared to more traditional parametric models, the proposed method is significantly more expressive and can reconstruct complex mass distributions, which we demonstrate by using realistic lensing galaxies taken from the IllustrisTNG cosmological hydrodynamic simulation.

2023-06-27

The Astrophysical Journal (published)

doi.org

arxiv.org

Beyond Gaussian Noise: A Generalized Approach to Likelihood Analysis with Non-Gaussian Noise

Ronan Legin