Related papers: Reconstruction procedures for two inverse scatteri…
We study the inverse backscattering problem for the Schr\"odinger equation in two dimensions. We prove that, for a non-smooth potential in 2D the main singularities up to 1/2 of the derivative of the potential are contained in the Born…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
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…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…
In nanoscale imaging technique and ultrafast laser, the reconstruction procedure is normally formulated as a blind phase retrieval (BPR) problem, where one has to recover both the sample and the probe (pupil) jointly from phaseless data.…
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…
Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…