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Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…
The resonant excitation of an electromagnetic guided mode of a slab structure by exterior radiation results in anomalous scattering behavior, including sharp energy-transmission anomalies and field amplification around the frequency of the…
In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of…
We consider a two-stage numerical procedure for imaging of objects buried in dry sand using time-dependent backscattering experimental radar measurements. These measurements are generated by a single point source of electric pulses and are…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced…
The far-field pattern of a simple one-dimensional laser array of emitters radiating into free space is considered. In the path of investigating the inverse problem for their near fields leading to a target beam form, surprisingly we found…
A deep learning-assisted inversion method is proposed to solve the inhomogeneous background imaging problem. Three non-iterative methods, namely the distorted-Born (DB) major current coefficients method, the DB modified Born approximation…
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main…
We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a…
We propose an inverse-design approach for computational spectrometers in which the scattering media are topology-optimized to achieve better performance in inference of unknown spectra. Unlike traditional end-to-end approaches, our inverse…
The goal of synthetic aperture imaging is to estimate the reflectivity of a remote region of interest by processing data gathered with a moving sensor which emits periodically a signal and records the backscattered wave. We introduce and…
This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
While scattered light conveys most of the information we perceive, scattering may also distort that information before it reaches our detectors. The problem is acute in many applications, such as in high-resolution microscopy of biological…
Inverse scattering problems without the phase information arise in imaging of nanostructures whose sizes are hundreds of nanometers as well as in imaging of biological cells. The governing equation is the 3-d generalized Helmholtz equation…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
In this paper, we study the inverse acoustic medium scattering problem to reconstruct the unknown inhomogeneous medium from far field patterns of scattered waves. We propose the reconstruction scheme based on the Kalman filter, which…
Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy-Lax formulation is developed to take fully into account of the…
This paper considers 3-D elastic scattering problems by penetrable obstacles with embedded objects. The well-posedness of transmission problem is proved by employing integral equation method. Then the Inverse Problems , which is to recover…