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Interpreting scattered acoustic and electromagnetic wave patterns is a computational task that enables remote imaging in a number of important applications, including medical imaging, geophysical exploration, sonar and radar detection, and…
We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…
Modern imaging techniques at the molecular scale rely on utilizing novel coherent light sources like X-ray free electron lasers for the ultimate goal of visualizing such objects as individual biomolecules rather than crystals. Here, unlike…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
We explore systematically a rigorous theory of the inverse scattering transforms with matrix Riemann-Hilbert problems for both focusing and defocusing modified Korteweg-de Vries (mKdV) equations with non-zero boundary conditions (NZBCs) at…
A new approach to the design of graded Photonic Crystals (GPCs) devices is proposed by exploiting the inverse scattering framework as a synthesis tool. The introduced general methodology can be applied to arbitrary far-field specifications,…
Infrared small target detection (ISTD) under complex backgrounds is a difficult problem, for the differences between targets and backgrounds are not easy to distinguish. Background reconstruction is one of the methods to deal with this…
Dataset Distillation aims to synthesize compact datasets that can approximate the training efficacy of large-scale real datasets, offering an efficient solution to the increasing computational demands of modern deep learning. Recently,…
Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all…
Due to manufacturing defects or wear and tear, industrial components may have uncertainties. In order to evaluate the performance of machined components, it is crucial to quantify the uncertainty of the scattering surface. This brings up an…
We propose a technique of compensating the spurious reflections implied by the multiple-scattering (MS) method, commonly used for analyzing finite photonic crystal (PC) systems, to obtain exact values of characteristic parameters, such as…
This paper proposes a novel approach to spectral computed tomography (CT) material decomposition that uses the recent advances in generative diffusion models (DMs) for inverse problems. Spectral CT and more particularly photon-counting CT…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
The development of medium-energy inelastic X-ray scattering (IXS) optics with meV and sub-meV resolution has attracted considerable efforts in recent years. Meanwhile, there are also concerns or debates about the fundamental and feasibility…
Forward scatter radar (FSR) has emerged as an effective imaging modality for target detection, utilizing forward scattering (FS) signals to reconstruct two-dimensional shadow profile images of objects. However, real-world FS signals are…
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…
Dynamic Contrast Enhanced-Magnetic Resonance Imaging (DCE-MRI) is widely used to complement ultrasound examinations and x-ray mammography during the early detection and diagnosis of breast cancer. However, images generated by various MRI…
Recently, deep learning-based compressive imaging (DCI) has surpassed the conventional compressive imaging in reconstruction quality and faster running time. While multi-scale has shown superior performance over single-scale, research in…
Multi-spectral CT (MSCT) is increasingly used in industrial non-destructive testing and medical diagnosis because of its outstanding performance like material distinguishability. The process of obtaining MSCT data can be modeled as…
Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The…