Related papers: Besov priors for Bayesian inverse problems

Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…

Bayesian observer and actor models have provided normative explanations for many behavioral phenomena in perception, sensorimotor control, and other areas of cognitive science and neuroscience. They attribute behavioral variability and…

We propose and study several inverse problems associated with the nonlinear progressive waves that arise in infrasonic inversions. The nonlinear progressive equation (NPE) is of a quasilinear form $\partial_t^2 u=\Delta f(x, u)$ with $f(x,…

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…

We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…

An evolutionary form of a generalized Bayesian update method, which is strictly derivative- free yet directed through an additive update term based purely on the statistical moments of the design variables, is proposed for nonlinear inverse…

In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…

We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies…

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…

This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks, line cracks and…

We consider the statistical inverse problem of estimating a background fluid flow field $\mathbf{v}$ from the partial, noisy observations of the concentration $\theta$ of a substance passively advected by the fluid, so that $\theta$ is…

We develop a data-driven algorithm for automatically selecting the regularisation parameter in Bayesian inversion under random tree Besov priors. One of the key challenges in Bayesian inversion is the construction of priors that are both…

In this article, the solution of a statistical inverse problem $M = AU+\mathcal{E}$ by the Bayesian approach is studied where $U$ is a function on the unit circle $\mathbb{T}$, i.e., a periodic signal. The mapping $A$ is a smoothing linear…

This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…

Diffusion models have emerged as a powerful foundation model for visual generations. With an appropriate sampling process, it can effectively serve as a generative prior for solving general inverse problems. Current posterior sampling-based…

We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…

We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…

In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a…

Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…