## What is/are Inverse Source?

Inverse Source - finite-element modeling, inverse source reconstruction, data-driven pattern recognition, and statistical correlation tomography, to reconstruct RSNs in dual contrasts of oxygenated (HbO) and deoxygenated hemoglobins (HbR).^{[1]}The main results of the analysis concern the space invariance of the PSF of the considered geometries, which means that resolution is the same over the whole investigation domain, and the appreciation of its values for the inverse source and scattering problems.

^{[2]}To regularize the inverse source problem, a mollification regularization method is applied.

^{[3]}Inverse source reconstruction problems offer great potential for applications of interest to engineering, such as the identification of polluting sources, and to medicine, such as electroencephalography, to cite at least two relevant examples.

^{[4]}Our goal is to solve the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves.

^{[5]}We prove global Lipschitz stability and conditional local Holder stability for inverse source and coefficient problems for a first-order linear hyperbolic equation, the coefficients of which depend on both space and time.

^{[6]}We analyze this approach with the help of two linear standard examples, namely the inverse source problem for the Poisson equation and the backwards heat equation, i.

^{[7]}In this contribution, we investigate an inverse source problem for a fractional diffusion and wave equation with the Caputo fractional derivative of the space-dependent variable order.

^{[8]}The aim of this work is to present a near-field FM for inverse source problems that have many applications.

^{[9]}We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium.

^{[10]}Moreover, the TPG method is applied to an inverse source problem for a non-smooth semilinear elliptic PDE where a Bouligand subdifferential can be used in place of the non-existing Gâteaux derivative, and the corresponding Bouligand two-point gradient iteration is shown to be a convergent regularization scheme.

^{[11]}In this article, we consider an inverse source problem for Poisson equation in a strip domain.

^{[12]}Identification of abnormal source hidden in distributed parameter systems (DPSs) belongs to the category of inverse source problems.

^{[13]}In this paper, homogenization functions are first proposed to address two-dimensional (2D) and three-dimensional (3D) inverse source problems of nonlinear time-fractional wave equation (ISPs-NTFWE).

^{[14]}We formulate the inverse source problem in.

^{[15]}In this work, we apply an adjoint technique to solve two-dimensional direct and inverse source-detector transport problems.

^{[16]}Inverse source and in particular inverse surface-source solutions can rather easily be obtained for irregularly sampled observation data collected with arbitrary measurement probes.

^{[17]}The aim of this article is to investigate the uniqueness of solution of an inverse source problem for a generalized kinetic equation on a Riemannian manifold.

^{[18]}The considered inverse problem can be called the inverse source problem.

^{[19]}This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion.

^{[20]}The conditional stability for the inverse source problem is investigated.

^{[21]}For the Greek earthquake, the tool predicted a deformation close to the InSAR product, and gave evidences of atmospheric disturbances, thus providing information for inverse source modelling.

^{[22]}We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data.

^{[23]}In this paper, a Cauchy problem of non-homogenous stochastic heat equation is considered together with its inverse source problem, where the source term is assumed to be driven by an additive white noise.

^{[24]}A closed-form evaluation of the PSF relevant to the inverse source problem is first provided.

^{[25]}We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data.

^{[26]}In this article, the inverse source problem is determined by the partition hyperbolic equation under the left end flux tension of the string, where the extra measurement is considered.

^{[27]}This paper is concerned with the inverse source problem of the time-harmonic elastic waves.

^{[28]}In this paper, the question of evaluating the dimension of data space in an inverse source problem from near-field phaseless data is addressed.

^{[29]}In this article, the performance of the inverse source method (ISM) for incident power density evaluation is investigated in terms of accuracy and operational costs, i.

^{[30]}This article deals with the classical question of estimating the achievable resolution in terms of the configuration parameters in inverse source problems.

^{[31]}The inverse source problem has a number of applications in antenna analysis and synthesis.

^{[32]}We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data.

^{[33]}This paper is concerned with the inverse source problem for the transport equation with external force.

^{[34]}Numerical results obtained with an inverse source solver for several antennas with aperture sizes of up to 1000 wavelengths are presented.

^{[35]}We apply the linearization technique and transform the direct problem into an inverse source problem.

^{[36]}This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions.

^{[37]}More in general, first, we consider the radiation properties of a collection of continuous linear sources by following an inverse source approach which aims at investigating the spectral decomposition of the relevant radiation operator by discussing its singular value decomposition and the number of degrees of freedom of the source according to its geometry.

^{[38]}This paper considers an inverse source location problem in a concrete block to address the mentioned issue, a proposed methodology which also has wider application in competitive data selection.

^{[39]}The uniqueness of a solution to this inverse source problem is proved, whilst counter examples are constructed to discuss the conditions under which uniqueness holds.

^{[40]}We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary.

^{[41]}The second part of this paper is concerned with the application of the newly developed accelerated iterative regularization methods to the diffusion-based bioluminescence tomography, which is modeled as an inverse source problem in elliptic partial differential equations with both Dirichlet and Neumann boundary data.

^{[42]}The results of the inverse source problem solution for an atmospheric chemistry transport and transformation model for in situ and remote sensing measurement data are compared.

^{[43]}This method can be applied to an inverse source problem for a non-smooth semilinear elliptic PDE where a Bouligand subdifferential can be used in place of the non-existing Fr\'echet derivative, and we show that the corresponding Bouligand-Levenberg-Marquardt iteration is an iterative regularization scheme.

^{[44]}Concerning the sparsity of the source term, we transform the inverse source problem into an elastic-net regularization optimization problem.

^{[45]}We establish the conditional stability for inverse source problems for a hyperbolic equation and a parabolic equation, and our method is widely applicable to various evolution equations.

^{[46]}In this paper, we prove Lipschitz stability results for the inverse source problem of determining the spatially varying factor in a source term in the Korteweg–de Vries–Burgers (KdVB) equation with mixed boundary conditions.

^{[47]}The accuracy of the obtained near-fields and far-fields depends more on the stopping criterion of the inverse source solver than on the particular choice of the equivalent surface-source representation, where the zero-field condition may influence the stopping criterion in a rather unpredictable way.

^{[48]}These conditions are verified for an inverse source problem for an elliptic PDE with a non-smooth Lipschitz continuous nonlinearity, showing that the corresponding Bouligand–Landweber iteration converges strongly for exact data as well as in the limit of vanishing data if the iteration is stopped according to the discrepancy principle.

^{[49]}Numerical results for image denoising and deblurring, inverse source, inverse heat conduction problems and second derivative problems have shown the effectiveness of the proposed model.

^{[50]}

## time fractional diffusion

For a multi-term time-fractional diffusion equation comprising Hilfer fractional derivatives in time variables of different orders between $ 0 $ and $ 1 $, we have studied two problems (direct problem and inverse source problem).^{[1]}This paper is concerned with an inverse source problem for a space-time fractional diffusion equation.

^{[2]}In this paper, we consider the inverse source problem for the time-fractional diffusion equation, which has been known to be an ill-posed problem.

^{[3]}In the paper, an inverse source problem for a time-fractional diffusion equation is formulated and proved.

^{[4]}In this paper, we are concerned with an inverse source problem for the time-fractional diffusion equation with variable coefficients in a general bounded domain.

^{[5]}This paper studies an inverse source problem for a time fractional diffusion equation with the distributed order Caputo derivative.

^{[6]}We study uniqueness of a solution for an inverse source problem arising in linear time-fractional diffusion equations with time dependent coefficients.

^{[7]}

## fractional diffusion equation

This research considers an inverse source problem for fractional diffusion equation that containing fractional derivative with non-singular and non-local kernel, namely, Atangana-Baleanu-Caputo fractional derivative.^{[1]}In this paper, we consider an inverse source problem for fractional diffusion equation with Riemann–Liouville derivative.

^{[2]}

## An Inverse Source

An inverse source problem approach is adopted, where solutions stable with respect to data uncertainties are to be found by relying on the analysis of the pertinent operator by the Singular Values Decomposition.^{[1]}An inverse source problem for time-harmonic Maxwell equation is studied and a direct sampling method to recover the location and the moments of electric current dipoles from nearand far-field data at a fixed frequency is developed.

^{[2]}An inverse source problem for elastic waves in isotropic homogeneous media is considered and a Fourier transform based multi-frequency approach to determine the elastic source is proposed.

^{[3]}

## inverse source problem

For a multi-term time-fractional diffusion equation comprising Hilfer fractional derivatives in time variables of different orders between $ 0 $ and $ 1 $, we have studied two problems (direct problem and inverse source problem).^{[1]}To regularize the inverse source problem, a mollification regularization method is applied.

^{[2]}Then the source location and its intensity function is calculated by solving inverse source problem using a geostatistical approach.

^{[3]}Our goal is to solve the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves.

^{[4]}We analyze this approach with the help of two linear standard examples, namely the inverse source problem for the Poisson equation and the backwards heat equation, i.

^{[5]}In this contribution, we investigate an inverse source problem for a fractional diffusion and wave equation with the Caputo fractional derivative of the space-dependent variable order.

^{[6]}The aim of this work is to present a near-field FM for inverse source problems that have many applications.

^{[7]}We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium.

^{[8]}This paper is concerned with an inverse source problem for a space-time fractional diffusion equation.

^{[9]}Moreover, the TPG method is applied to an inverse source problem for a non-smooth semilinear elliptic PDE where a Bouligand subdifferential can be used in place of the non-existing Gâteaux derivative, and the corresponding Bouligand two-point gradient iteration is shown to be a convergent regularization scheme.

^{[10]}In this article, we consider an inverse source problem for Poisson equation in a strip domain.

^{[11]}Identification of abnormal source hidden in distributed parameter systems (DPSs) belongs to the category of inverse source problems.

^{[12]}In this paper, homogenization functions are first proposed to address two-dimensional (2D) and three-dimensional (3D) inverse source problems of nonlinear time-fractional wave equation (ISPs-NTFWE).

^{[13]}We formulate the inverse source problem in.

^{[14]}The aim of this article is to investigate the uniqueness of solution of an inverse source problem for a generalized kinetic equation on a Riemannian manifold.

^{[15]}The considered inverse problem can be called the inverse source problem.

^{[16]}This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion.

^{[17]}This research considers an inverse source problem for fractional diffusion equation that containing fractional derivative with non-singular and non-local kernel, namely, Atangana-Baleanu-Caputo fractional derivative.

^{[18]}Also, we prove similar results for the corresponding inverse source problem.

^{[19]}The conditional stability for the inverse source problem is investigated.

^{[20]}We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data.

^{[21]}In this paper, we consider the inverse source problem for the time-fractional diffusion equation, which has been known to be an ill-posed problem.

^{[22]}In this paper, a Cauchy problem of non-homogenous stochastic heat equation is considered together with its inverse source problem, where the source term is assumed to be driven by an additive white noise.

^{[23]}A closed-form evaluation of the PSF relevant to the inverse source problem is first provided.

^{[24]}We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data.

^{[25]}In this article, the inverse source problem is determined by the partition hyperbolic equation under the left end flux tension of the string, where the extra measurement is considered.

^{[26]}This paper is concerned with the inverse source problem of the time-harmonic elastic waves.

^{[27]}In this paper, the question of evaluating the dimension of data space in an inverse source problem from near-field phaseless data is addressed.

^{[28]}This article deals with the classical question of estimating the achievable resolution in terms of the configuration parameters in inverse source problems.

^{[29]}The inverse source problem has a number of applications in antenna analysis and synthesis.

^{[30]}We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data.

^{[31]}An inverse source problem approach is adopted, where solutions stable with respect to data uncertainties are to be found by relying on the analysis of the pertinent operator by the Singular Values Decomposition.

^{[32]}This paper is concerned with the inverse source problem for the transport equation with external force.

^{[33]}We apply the linearization technique and transform the direct problem into an inverse source problem.

^{[34]}This work deals with a geometric inverse source problem.

^{[35]}In the paper, an inverse source problem for a time-fractional diffusion equation is formulated and proved.

^{[36]}In this paper, we consider an inverse source problem for fractional diffusion equation with Riemann–Liouville derivative.

^{[37]}This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions.

^{[38]}An inverse source problem for time-harmonic Maxwell equation is studied and a direct sampling method to recover the location and the moments of electric current dipoles from nearand far-field data at a fixed frequency is developed.

^{[39]}The uniqueness of a solution to this inverse source problem is proved, whilst counter examples are constructed to discuss the conditions under which uniqueness holds.

^{[40]}An inverse source problem for elastic waves in isotropic homogeneous media is considered and a Fourier transform based multi-frequency approach to determine the elastic source is proposed.

^{[41]}We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary.

^{[42]}The second part of this paper is concerned with the application of the newly developed accelerated iterative regularization methods to the diffusion-based bioluminescence tomography, which is modeled as an inverse source problem in elliptic partial differential equations with both Dirichlet and Neumann boundary data.

^{[43]}The results of the inverse source problem solution for an atmospheric chemistry transport and transformation model for in situ and remote sensing measurement data are compared.

^{[44]}This method can be applied to an inverse source problem for a non-smooth semilinear elliptic PDE where a Bouligand subdifferential can be used in place of the non-existing Fr\'echet derivative, and we show that the corresponding Bouligand-Levenberg-Marquardt iteration is an iterative regularization scheme.

^{[45]}Concerning the sparsity of the source term, we transform the inverse source problem into an elastic-net regularization optimization problem.

^{[46]}We establish the conditional stability for inverse source problems for a hyperbolic equation and a parabolic equation, and our method is widely applicable to various evolution equations.

^{[47]}In this paper, we prove Lipschitz stability results for the inverse source problem of determining the spatially varying factor in a source term in the Korteweg–de Vries–Burgers (KdVB) equation with mixed boundary conditions.

^{[48]}Among them, very recently a new approach has been proposed for the case of bi-dimensional geometries and scalar field, based on the concept of joint sparsity and the solution of related inverse source problems.

^{[49]}These conditions are verified for an inverse source problem for an elliptic PDE with a non-smooth Lipschitz continuous nonlinearity, showing that the corresponding Bouligand–Landweber iteration converges strongly for exact data as well as in the limit of vanishing data if the iteration is stopped according to the discrepancy principle.

^{[50]}

## inverse source reconstruction

finite-element modeling, inverse source reconstruction, data-driven pattern recognition, and statistical correlation tomography, to reconstruct RSNs in dual contrasts of oxygenated (HbO) and deoxygenated hemoglobins (HbR).^{[1]}Inverse source reconstruction problems offer great potential for applications of interest to engineering, such as the identification of polluting sources, and to medicine, such as electroencephalography, to cite at least two relevant examples.

^{[2]}This means that the inverse problem of MAET-MI can be transformed into an inverse source reconstruction of a wave equation based on the coil detection.

^{[3]}

## inverse source solver

Numerical results obtained with an inverse source solver for several antennas with aperture sizes of up to 1000 wavelengths are presented.^{[1]}The accuracy of the obtained near-fields and far-fields depends more on the stopping criterion of the inverse source solver than on the particular choice of the equivalent surface-source representation, where the zero-field condition may influence the stopping criterion in a rather unpredictable way.

^{[2]}

## inverse source method

In this article, the performance of the inverse source method (ISM) for incident power density evaluation is investigated in terms of accuracy and operational costs, i.^{[1]}In this work, we investigate inverse source methods with respect to their imaging capabilities.

^{[2]}