Related papers: A Weighted Sampling Method for Inverse Medium Prob…

We introduce the sparse direct sampling method (DSM) to estimate properties of a region from signals that probe the region. We demonstrate the sparse-DSM on two separate problems: estimating both the angle-of-arrival of a radio wave…

In this work, we apply the Bayesian approach for the acoustic scattering problem to reconstruct the shape of a sound-soft obstacle using the limited-aperture far-field measure data. A novel total variation prior is assigned to the shape…

We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced…

In this paper, we study the inverse medium scattering problem to reconstruct unknown inhomogeneous medium from far field patterns of scattered waves. In the first part of our work, the linear inverse scattering problem was discussed, while…

The recently developed globally convergent numerical method for an inverse medium problem for the Helmholtz equation is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the…

This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source…

We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…

Using measure theoretic arguments, we provide a general framework for describing and studying the general linear inverse dispersion problem where no a priori assumptions on the source function has been made. We investigate the source-sensor…

The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively…

Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…

This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…

We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

Estimating the parameters of compact binaries which coalesce and produce gravitational waves is a challenging Bayesian inverse problem. Gravitational-wave parameter estimation lies within the class of multifidelity problems, where a variety…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Most recent machine learning research focuses on developing new classifiers for the sake of improving classification accuracy. With many well-performing state-of-the-art classifiers available, there is a growing need for understanding…

Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency…

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…

A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…

This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…