Related papers: On inverse problems in multi-population aggregatio…
We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific…
The problem of mixed signals occurs in many different contexts; one of the most familiar being acoustics. The forward problem in acoustics consists of finding the sound pressure levels at various detectors resulting from sound signals…
Tomographic imaging is in general an ill-posed inverse problem. Typically, a single regularized image estimate of the sought-after object is obtained from tomographic measurements. However, there may be multiple objects that are all…
Variational inference is a general framework to obtain approximations to the posterior distribution in a Bayesian context. In essence, variational inference entails an optimization over a given family of probability distributions to choose…
In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…
In this paper we extend our recent work on two-dimensional (2D) diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux…
Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…
Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix…
This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Inverse problems, where the goal is to recover an unknown signal from noisy or incomplete measurements, are central to applications in medical imaging, remote sensing, and computational biology. Diffusion models have recently emerged as…
Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating the distribution of optical parameters inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic…
Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…