Related papers: Imaging point sources in heterogeneous environment…
We present a novel study on enhancing the capability of preserving the content in world models, focusing on a property we term World Stability. Recent diffusion-based generative models have advanced the synthesis of immersive and realistic…
We introduce a new approach for measuring both the effective medium and the transport properties of light propagation in heterogeneous media. Our method utilizes the conceptual equivalence of frequency variation with a change in the…
This paper is concerned with the stability issue in determining absorption and diffusion coefficients in photoacoustic imaging. Assuming that the medium is layered and the acoustic wave speed is known we derive global H\"{o}lder stability…
In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for…
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
Metalenses have emerged as a powerful platform for compact wavefront engineering; however, their performance stability under refractive index fluctuations induced by environmental perturbations, such as temperature shifts, remains a…
In this paper we study the uniqueness and the increasing stability in the inverse source problem for electromagnetic waves in homogeneous and inhomogeneous media from boundary data at multiple wave numbers. For the unique determination of…
We present a rigorous mathematical solution to photometric redshift estimation and the more general inversion problem. The challenge we address is to meaningfully constrain unknown properties of astronomical sources based on given…
Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the…
Recently, differentiable volume rendering in neural radiance fields (NeRF) has gained a lot of popularity, and its variants have attained many impressive results. However, existing methods usually assume the scene is a homogeneous volume so…
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…
This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…