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Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…
This paper is concerned with the inverse medium problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering…
It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location…
Distributed Acoustic Sensing (DAS) is a novel technology that allows sampling of the seismic wavefield densely over a broad frequency band. This makes it an ideal tool for surface wave studies. In this study, we evaluate the potential of…
Full-waveform inversion (FWI) is an advanced technique for reconstructing high-resolution subsurface physical parameters by progressively minimizing the discrepancy between observed and predicted seismic data. However, conventional FWI…
Established image recovery methods in fast ultrasound imaging, e.g. delay-and-sum, trade the image quality for the high frame rate. Cutting-edge inverse scattering methods based on compressed sensing (CS) disrupt this tradeoff via a priori…
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…
In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the…
The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…
Wavefront-free behavior and the resulting quantification difficulties are intrinsic limitations of vibrothermography due to the diffusive nature of thermal fields. This work proposes a generalized virtual wave reconstruction framework to…
An inverse iterative algorithm for microwave imaging based on moment method solution is presented here. The iterative scheme has been developed on constrained optimization technique and is certain to converge. Different mesh size for the…
This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
Mathematically rigorous inversion method is developed to recover compactly supported potentials from the fixed-energy scattering data in three dimensions. Error estimates are given for the solution. An algorithm for inversion of noisy…
An optical imager that exploits off-center image rotation to encode both the lateral and depth coordinates of point sources in a single snapshot can perform 3D localization and tracking of space debris. When actively illuminated, unresolved…
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…
Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…
We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \ \mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in the Maxwell's equations,…
This study concentrates on advancing mathematical and computational methodology for radar tomography imaging in which the unknown volumetric velocity distribution of a wave within a bounded domain is to be reconstructed. Our goal is to…
The correct insertion of virtual objects in images of real-world scenes requires a deep understanding of the scene's lighting, geometry and materials, as well as the image formation process. While recent large-scale diffusion models have…