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We present an imaging technique particularly suited to the detection of a target embedded in a strongly scattering medium. Classical imaging techniques based on the Born approximation fail in this kind of configuration because of multiply…
This paper introduces a novel matrix-free approach for full waveform inversion in anisotropic elastic media, incorporating density variation through the utilization of the distorted Born iterative method. This study aims to overcome the…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the…
In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…
We introduce a novel nonlinear seismic imaging method based on model order reduction. The reduced order model (ROM) is an orthogonal projection of the wave equation propagator operator on the subspace of the snapshots of the solutions of…
Digital array orthogonal transformations that can be presented as a decomposition over basis items or basis images are considered. The orthogonal transform provides digital data scattering, a process of pixel energy redistributing, that is…
Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…
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…
We present a physically intuitive matrix approach for wave imaging and characterization in scattering media. The experimental proof-of-concept is performed with ultrasonic waves, but this approach can be applied to any field of wave physics…
We introduce a novel reflection-mode diffraction tomography technique that enables simultaneous recovery of forward and backward scattering information for high-resolution 3D refractive index reconstruction. Our technique works by imaging a…
The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive indicators of the onset of material damage. However, these effects are usually very small and can be detected only using cumbersome…
Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…
Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that…
The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretable machine learning…
In this paper, a linear model based on multiple measurement vectors model is proposed to formulate the inverse scattering problem of highly conductive objects at one single frequency. Considering the induced currents which are mostly…
Rotating Synthetic Aperture Radar (ROSAR) can generate a 360$^\circ$ image of its surrounding environment using the collected data from a single moving track. Due to its non-linear track, the Back-Projection Algorithm (BPA) is commonly used…
The Transfer Matrix Method is a powerful numerical tool for simulating wave propagation in layered media. It has been widely applied in many fields, although its use is typically restricted to passive media. In this paper, we develop the…