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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 propose an end-to-end deep learning framework that comprehensively solves the inverse wave scattering problem across all length scales. Our framework consists of the newly introduced wide-band butterfly network coupled with a simple…
This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some…
In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…
A new algorithm for the stable solution of a three-dimensional scalar inverse problem of acoustic sounding of an inhomogeneous medium in a cylindrical region is proposed. The data of the problem is the complex amplitude of the wave field,…
Solving the wave equation is essential to seismic imaging and inversion. The numerical solution of the Helmholtz equation, fundamental to this process, often encounters significant computational and memory challenges. We propose an…
Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…
A new algorithm is proposed for solving the three-dimensional scalar inverse problem of acoustic sounding in an inhomogeneous medium. The data for the algorithm are the complex amplitudes of the wave field measured outside the inhomogeneity…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
Low-count positron emission tomography (PET) reconstruction is a challenging inverse problem due to severe degradations arising from Poisson noise, photon scarcity, and attenuation correction errors. Existing deep learning methods typically…
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…
In portable, 3-D, or ultra-fast ultrasound (US) imaging systems, there is an increasing demand to reconstruct high quality images from limited number of data. However, the existing solutions require either hardware changes or…
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields, and many scientists strive to solve them in an efficient and robust manner. In this paper, we propose an interpretable neural solver, the…
Fourier embedding has shown great promise in removing spectral bias during neural network training. However, it can still suffer from high generalization errors, especially when the labels or measurements are noisy. We demonstrate that…
Deep learning methods are emerging as popular computational tools for solving forward and inverse problems in traffic flow. In this paper, we study a neural operator framework for learning solutions to nonlinear hyperbolic partial…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…
In this letter, a fast Fourier transform (FFT)-enhanced low-complexity super-resolution sensing algorithm for near-field source localization with both angle and range estimation is proposed. Most traditional near-field source localization…
This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear),…
This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…