Related papers: Bayesian reconstruction of the cosmological large-…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
Using higher-order statistics to capture cosmological information from weak lensing surveys often requires a transformation of observed shear to a measurement of the convergence signal. This inverse problem is complicated by noise and…
The linear algorithm of the Wiener filter and constrained realizations (CRs) of Gaussian random fields is extended here to perform non-linear CRs. The procedure consists of: (1) Using low resolution data to constrain a high resolution…
We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a non-Poisson likelihood including a deterministic…
In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…
Microscopy is a powerful visualization tool in biology, enabling the study of cells, tissues, and the fundamental biological processes; yet, the observed images typically suffer from blur and background noise. In this work, we propose a…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
We present a self-consistent Bayesian formalism to sample the primordial density fields compatible with a set of dark matter density tracers after cosmic evolution observed in redshift space. Previous works on density reconstruction did not…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
We discuss the implementation of Bayesian inversion methods in order to recover the properties of the intergalactic medium from observations of the neutral hydrogen Lyman-$\alpha$ absorptions observed in the spectra of high redshift quasars…
Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework…
This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
The dark sirens method combines gravitational waves and catalogs of galaxies to constrain the cosmological expansion history, merger rates and mass distributions of compact objects, and the laws of gravity. However, the incompleteness of…
Solving large-scale Bayesian inverse problems presents significant challenges, particularly when the exact (discretized) forward operator is unavailable. These challenges often arise in image processing tasks due to unknown defects in the…
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the…
Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…
Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior…