Related papers: Bayesian reconstruction of the cosmological large-…
A method for the reconstruction of the primordial density fluctuation field is presented. Various previous approaches to this problem rendered {\it non-unique} solutions. Here, it is demonstrated that the initial positions of dark matter…
Efficient assessment of convolved hidden Markov models is discussed. The bottom-layer is defined as an unobservable categorical first-order Markov chain, while the middle-layer is assumed to be a Gaussian spatial variable conditional on the…
We investigate the regularizing behavior of an iterative Krylov subspace method for the solution of linear inverse problems in precisions lower than double. Recent works have considered the projection of iterated Tikhonov methods using…
This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson…
We present an efficient implementation of Wiener filtering of real-space linear field and optimal quadratic estimator of its power spectrum Band-powers. We first recast the field reconstruction into an optimization problem, which we solve…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
Deploying 3D single-photon Lidar imaging in real world applications faces multiple challenges including imaging in high noise environments. Several algorithms have been proposed to address these issues based on statistical or learning-based…
We present a Bayesian Voronoi image reconstruction technique (VIR) for interferometric data. Bayesian analysis applied to the inverse problem allows us to derive the a-posteriori probability of a novel parameterization of interferometric…
The sparse layouts of radio interferometers result in an incomplete sampling of the sky in Fourier space which leads to artifacts in the reconstructed images. Cleaning these systematic effects is essential for the scientific use of…
We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…
Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…
We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretisation of Hamiltonian equations of motion (EoM). This is achieved by…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
In this paper, we investigate the problem of inverse electromagnetic scattering to recover multilayer human tissue profiles using ultrawideband radar systems in a Bayesian setting. We study the recovery problem in a blind setting, in which…
A way of constructing a nonlinear filter close to the optimal Kolmogorov - Wiener filter is proposed within the framework of the statistical approach to inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions, produces…