Related papers: A Weighted Sampling Method for Inverse Medium Prob…
In the analysis of survey data, sampling weights are needed for consistent estimation of the population. However, the original inverse probability weights from the survey sample design are typically modified to account for non-response, to…
We are concerned with the inverse scattering problems associated with incomplete measurement data. It is a challenging topic of increasing importance in many practical applications. Based on a prototypical working model, we propose a…
We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous medium from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed and nonlinear, and the iterative…
This study presents a frequency-domain, Hessian-free ray-Born inversion method for quantitative ultrasound tomography, extending the author's previous Hessian-based approach. Both approaches model acoustic wave propagation using a ray-based…
An optimal mesh size of the sampling region can help to reduce computational burden in practical applications. In this work, we investigate optimal choices of mesh sizes for the identifications of medium obstacles from either the far-field…
Inverse scattering methods capable of compressive imaging are proposed and analyzed. The methods employ randomly and repeatedly (multiple-shot) the single-input-single-output (SISO) measurements in which the probe frequencies, the incident…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
Suppose an $n \times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \ll n$ of the responses, and then produce a…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…
Training neural samplers directly from unnormalized densities without access to target distribution samples presents a significant challenge. A critical desideratum in these settings is achieving comprehensive mode coverage, ensuring the…
In many modern imaging applications the desire to reconstruct high resolution images, coupled with the abundance of data from acquisition using ultra-fast detectors, have led to new challenges in image reconstruction. A main challenge is…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
Non-invasive detection of objects embedded inside an optically scattering medium is essential for numerous applications in engineering and sciences. However, in most applications light at visible or near-infrared wavebands is scattered by…
We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
In imaging inverse problems, one seeks to recover an image from missing/corrupted measurements. Because such problems are ill-posed, there is great motivation to quantify the uncertainty induced by the measurement-and-recovery process.…
In this work, we focus on the inverse medium scattering problem (IMSP), which aims to recover unknown scatterers based on measured scattered data. Motivated by the efficient direct sampling method (DSM) introduced in [23], we propose a…