In this manuscript, the Cauchy problem of the modified Helmholtz equation is researched. This inverse problem is a serious ill-posed problem. The classical Landweber iterative regularization method is designed to find the regularized solution of this...
Light field imaging involves reconstructing a 4D light field from a 3D focal stack, which makes it challenging to reconstruct the light field from incomplete projection data. To address this problem, a linear projection system is established to model...
In this paper, we consider the inverse problem for the time-fractional Schrödinger equation. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. We use the fractional Landweber iterative regular...
In this paper, we study an inverse problem to identify the initial value problem of the homogeneous Rayleigh–Stokes equation for a generalized second-grade fluid with the Riemann–Liouville fractional derivative model. This problem is ill posed; that...
In this article, the inverse problem for identifying the space-dependent source of time fractional diffusion equation on a spherically symmetric domain with Caputo–Fabrizio fractional derivative is discussed. This problem is a typical ill-posed...
In this paper, Landweber iteration with a relaxation factor is proposed to solve nonlinear ill-posed integral equations. A compression multiscale Galerkin method that retains the properties of the Landweber iteration is used to discretize the Landweb...
Steel-reinforced concrete decks are prominently utilized in various civil structures such as bridges and railways, where they are susceptible to unforeseen impact forces during their operational lifespan. The precise identification of the impact even...
The Landweber iteration method is one of the most popular methods for the solution of linear discrete ill-posed problems. The diversity of physical problems and the diversity of operators that result from them leads us to think about updating the mai...
In this manuscript, we study the inverse problem for identifying the initial value of a time-fractional diffusion equation in an axisymmetric region. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. We choose...
In this paper, the inverse problem of identifying the source term of the time fractional diffusion-wave equation is studied. This problem is ill-posed, i.e., the solution (if it exists) does not depend on the measurable data. Under the priori bound c...
In aeromagnetic detection and geomagnetic navigation, the reference geomagnetic maps usually need to be continued to different altitudes. Traditionally, the geomagnetic field upward continuation is stable. Nevertheless, the downward continuation is i...
In this paper, we consider a generalized inexact Newton-Landweber iteration to solve nonlinear ill-posed inverse problems in Banach spaces, where the forward operator might not be Gâteaux differentiable. The method is designed with non-smooth c...
In this paper, the inverse problems for the boundary value and initial value in a heat equation are posed and solved. It is well known that those problems are ill posed. The problems are reformulated as integral equations of the first kind by using t...
Variable aperture sampling reconstruction matrices have a history of being computationally intensive due to the need to compute a full matrix inverse. In the field of remote sensing, several spaceborne radiometers and scatterometers, which have irreg...
This article considers the numerical solution of the direct and inverse problems of the gas lift process in oil production, described by a system of hyperbolic equations. The inverse problem is reduced to an optimal control problem, where the control...
Electrical impedance tomography (EIT) is non-destructive monitoring technology that can visualize the conductivity distribution in the observed area. The inverse problem for imaging is characterized by a serious nonlinear and ill-posed nature, which...
This study investigated the potential of the generative adversarial neural network (cGAN) image reconstruction in industrial electrical capacitance tomography. The image reconstruction quality was examined using image patterns typical for a two-phase...
The paper proposes a capacitance-sensor-array-based imaging system to detect water leakage inside insulating slabs with porous cells, such as anechoic acoustic rubber tiles. The modeling is conducted by using the finite element method to obtain the e...
A hybrid inversion scheme for through-the-wall imaging is proposed in this paper. The approach is based on a linearized model of the inverse-scattering problem, employing the Green’s function developed for a layered background. The reconstruction is...