Related papers: Data completion algorithms and their applications …
We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A…
Inverse scattering problems, such as those in electromagnetic imaging using phaseless data (PD-ISPs), involve imaging objects using phaseless measurements of wave scattering. Such inverse problems can be highly non-linear and ill-posed…
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…
Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…
Consider the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with complex refractive index. We show that an approximate factorization method can be applied to reconstruct the support of the complex…
A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the…
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…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…
This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…
We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…
Inverse scattering involving microwave and ultrasound waves require numerical solution of nonlinear optimization problem. To alleviate the computational burden of a full three-dimensional (3-D) inverse problem, it is a common practice to…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…
The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In…
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…
In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of…