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A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier--Nystr\"om discretization…
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…
Resonant ultrasound spectroscopy (RUS) is a powerful technique for measuring the full elastic tensor of a given material in a single experiment. Previously, this technique was limited to regularly-shaped samples such as rectangular…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
This paper is concerned with the problem of estimating (interpolating and smoothing) the shape (pose and the six modes of deformation) of a slender flexible body from multiple camera measurements. This problem is important in both biology,…
Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…
Important problems in wireless networks can often be solved by computing fixed points of standard or contractive interference mappings, and the conventional fixed point algorithm is widely used for this purpose. Knowing that the mapping…
In this work we describe a fast and stable algorithm for the computation of the orthogonal moments of an image. Indeed, orthogonal moments are characterized by a high discriminative power, but some of their possible formulations are…
We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor, once we know its symmetry class. In other words, we produce a rotation which brings an Elasticity tensor onto its normal form, given its…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
We construct non-trivial continuous isospectral deformations of Riemannian metrics on the ball and on the sphere in $\R^n$ for every $n\geq 9$. The metrics on the sphere can be chosen arbitrarily close to the round metric; in particular,…
Computer model calibration is a crucial step in building a reliable computer model. In the face of massive physical observations, a fast estimation for the calibration parameters is urgently needed. To alleviate the computational burden, we…
Modal expansion is an attractive technique for solving electromagnetic scattering problems. With the one set of resonator modes, calculated once and for all, any configuration of near-field or far-field sources can be obtained almost…
By idealizing a general mapping as a series of local affine ones, we derive approximately transformed material parameters necessary to control solid elastic waves within classical elasticity theory. The transformed elastic moduli are…
With the development of terahertz time-domain spectroscopy, methods have been proposed to precisely estimate the thickness, refractive index, and attenuation coefficient of a sample. In this article, we propose a new method to compute these…
This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…
We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…
Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…