Related papers: Bayesian reconstruction of the cosmological large-…
We investigate several approaches to address the inverse problem that arises in the limited inverse Fourier transform (L-IDFT) of quasi-distributions. The methods explored include Tikhonov regularization, the Backus-Gilbert method, the…
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…
Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
We present COSMIC BIRTH: COSMological Initial Conditions from Bayesian Inference Reconstructions with THeoretical models: an algorithm to reconstruct the primordial and evolved cosmic density fields from galaxy surveys on the light-cone.…
Iterative Krylov projection methods have become widely used for solving large-scale linear inverse problems. However, methods based on orthogonality include the computation of inner-products, which become costly when the number of…
We develop the maximum-entropy weak shear mass reconstruction method presented in earlier papers by taking each background galaxy image shape as an independent estimator of the reduced shear field and incorporating an intrinsic smoothness…
This note addresses possible applications of the Tikhonov regularization to image reconstruction of gravitational lens systems. Several modifications of the regularization algorithm are discussed. Our illustrative example is the close…
We present a novel method for reconstructing weak lensing mass or convergence maps as a probe to study non-Gaussianities in the cosmic density field. While previous surveys have relied on a flat-sky approximation, the forthcoming stage IV…
Coherent techniques for searches of gravitational-wave bursts effectively combine data from several detectors, taking into account differences in their responses. The efforts are now focused on the maximum likelihood principle as the most…
We present a new approach for nonlocal image denoising, based around the application of an unnormalized extended Gaussian ANOVA kernel within a bilevel optimization algorithm. A critical bottleneck when solving such problems for…
Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…
In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…
Motivated by recent developments in perturbative calculations of the nonlinear evolution of large-scale structure, we present an iterative algorithm to reconstruct the initial conditions in a given volume starting from the dark matter…
Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction…
This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying…
We develop technique concerning statistical analyses of the large-scale structure of the universe in the presence of biasing in the structure formation. We formulate the diagrammatic method to calculate the correlation functions of the…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…
Weak lensing observations measure the shear field and hence the gradient of the dimensionless surface density $\kappa$. We present several new algorithms to recover $\kappa$ {}from shear estimates on a finite region and compare how they…