Related papers: Advancing inverse scattering with surrogate modeli…

We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…

The quantification of uncertainties of computer simulations due to input parameter uncertainties is paramount to assess a model's credibility. For computationally expensive simulations, this is often feasible only via surrogate models that…

Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

This work describes a Bayesian framework for reconstructing the boundaries that represent targeted features in an image, as well as the regularity (i.e., roughness vs. smoothness) of these boundaries.This regularity often carries crucial…

In complex large-scale systems such as climate, important effects are caused by a combination of confounding processes that are not fully observable. The identification of sources from observations of system state is vital for attribution…

We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is…

We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…

Optical imaging through complex media, such as biological tissues or fog, is challenging due to light scattering. In the multiple scattering regime, wavefront shaping provides an effective method to retrieve information; it relies on…

Inverse scattering is a fundamental challenge in many imaging applications, ranging from microscopy to remote sensing. Solving this problem often requires jointly estimating two unknowns -- the image and the scattering field inside the…

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…

High-fidelity spectrum cartography is pivotal for spectrum management and wireless situational awareness, yet it remains a challenging ill-posed inverse problem due to the sparsity and irregularity of observations. Furthermore, existing…

In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…

In the context of structural health monitoring (SHM), the selection and extraction of damage-sensitive features from raw sensor recordings represent a critical step towards solving the inverse problem underlying the identification of…

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward…

We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…