Related papers: Convergence and Stability of the Inverse Scatterin…
This work studies an inverse scattering problem when limited-aperture data are available that are from just one or a few incident fields. This inverse problem is highly ill-posed due to the limited receivers and a few incident fields…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color…
Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…
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…
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…
We study wave scattering from a gently curved surface. We show that the recursive relations, implied by shift invariance, among the coefficients of the perturbative series for the scattering amplitude allow to perform an infinite…
We study imaging with an array of sensors that probes a medium with single frequency electromagnetic waves and records the scattered electric field. The medium is known and homogenous except for some small and penetrable inclusions. The…
In this work we shall review the (phased) inverse scattering problem and then pursue the phaseless reconstruction from far-field data with the help of the concept of scattering coefficients. We perform sensitivity, resolution and stability…
The problem of inpainting involves reconstructing the missing areas of an image. Inpainting has many applications, such as reconstructing old damaged photographs or removing obfuscations from images. In this paper we present the directional…
Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…
Coherent backscattering is a coherence effect in the propagation of waves through disordered media involving two or more scattering events. Here, we report on the observation of coherent backscattering from individual atoms and their mirror…
Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. Here, we discuss a sparse approximation method for computational time-reversal imaging. The method is formulated…
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method…
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as…
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…
Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…