Related papers: Posterior samples of source galaxies in strong gra…
Score-based models can serve as expressive, data-driven priors for scientific inverse problems. In strong gravitational lensing, they enable posterior inference of a background galaxy from its distorted, multiply-imaged observation.…
Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into…
We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined…
In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…
Reconstructing the initial conditions of the universe is a key problem in cosmology. Methods based on simulating the forward evolution of the universe have provided a way to infer initial conditions consistent with present-day observations.…
Examining the detailed structure of galaxy populations provides valuable insights into their formation and evolution mechanisms. Significant barriers to such analysis are the non-trivial noise properties of real astronomical images and the…
The inverse imaging task in radio interferometry is a key limiting factor to retrieving Bayesian uncertainties in radio astronomy in a computationally effective manner. We use a score-based prior derived from optical images of galaxies to…
Gravitational lensing is the phenomenon arising when light rays are deflected by the mass between the source and the observer. Largely magnified and highly distorted images of background galaxies are formed by these angular deflections if…
Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…
Given a noisy linear measurement $y = Ax + \xi$ of a distribution $p(x)$, and a good approximation to the prior $p(x)$, when can we sample from the posterior $p(x \mid y)$? Posterior sampling provides an accurate and fair framework for…
In this paper, we propose a unified framework of denoising score-based models in the context of graduated non-convex energy minimization. We show that for sufficiently large noise variance, the associated negative log density -- the energy…
Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function of complex, high-dimensional, non-Gaussian, and anisotropic noise. This is a major limitation for…
We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based…
Posterior sampling in high-dimensional spaces using generative models holds significant promise for various applications, including but not limited to inverse problems and guided generation tasks. Despite many recent developments,…
Score-based diffusion models have significantly advanced high-dimensional data generation across various domains, by learning a denoising oracle (or score) from datasets. From a Bayesian perspective, they offer a realistic modeling of data…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
We present a machine learning method for the reconstruction of the undistorted images of background sources in strongly lensed systems. This method treats the source as a pixelated image and utilizes the Recurrent Inference Machine (RIM) to…
We propose a score-based generative algorithm for sampling from power-scaled priors and likelihoods within the Bayesian inference framework. Our algorithm enables flexible control over prior-likelihood influence without requiring retraining…
Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a probabilistic forward modeling approach to…