Search

This paper is concerned with an inverse scattering problem of reconstructing a sound-soft obstacle for a Helmholtz system. Based on the interior resonant modes, we develop an efficient imaging scheme for determining the shape of the unknown scatterer. To begin with, we determine the interior eigenvalues of the scatterer by using the linear sampling method from its far-field measurements. Furthermore, the corresponding eigenfunctions can be determined by solving a constrained-optimization problem. Finally, using the reconstructed interior eigenfunctions, we propose an efficient Newton iterative formula to identify the shape of the obstacle. In order to reduce the sensitivity of initial value selection, we also present a multi-frequency Newton-type iterative algorithm. Further, local convergence justifications are provided to show the feasibility of the proposed approaches. Numerical experiments are presented to illustrate the effectiveness and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference sources to the inverse source model, we develop a novel strategy for recovering the phase information of far-field data. This reference source technique leads to an easy-to-implement phase retrieval formula. Mathematically, the stability of the phase retrieval approach is rigorously justified. Then we employ the Fourier method to deal with the multi-frequency inverse source problem with recovered phase information. Finally, some two and three dimensional numerical results are presented to demonstrate the viability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with a practical inverse problem of simultaneously reconstructing the surface heat flux and the thickness of a solid structure from the associated ultrasonic measurements. In a thermoacoustic coupling model, the thermal boundary condition and the thickness of a solid structure are both unknown, while the measurements of the propagation time by ultrasonic sensors are given. We reformulate the inverse problem as a PDE-constrained optimization problem by constructing a proper objective functional. We then develop an alternating iteration scheme which combines the conjugate gradient method and the deepest decent method to solve the optimization problem. Rigorous convergence analysis is provided for the proposed numerical scheme. By using experimental real data from the lab, we conduct extensive numerical experiments to verify several promising features of the newly developed method. [ABSTRACT FROM AUTHOR]

This paper concerns the direct sampling method for solving the inverse problem of identifying point sources for the Helmholtz equation from far-field data. We develop some novel indicator functions which could determine the locations and intensities of the target multipolar sources with a single wavenumber. Theoretically, the indicating behaviors are rigorously analyzed. Two- and three-dimensional numerical experiments are conducted to illustrate the effectiveness and robustness of the proposed approach. [ABSTRACT FROM AUTHOR]

We consider the inverse problem of determining an unknown vectorial source current distribution associated with the homogeneous Maxwell system. We propose a novel non-iterative reconstruction method for solving the aforementioned inverse problem from multi-frequency far-field measurements. The method is based on recovering the Fourier coefficients of the unknown source. A key ingredient of the method is to establish the relationship between the Fourier coefficients and the multi-frequency far-field data. Uniqueness and stability results are established for the proposed reconstruction method. Numerical experiments are presented to illustrate the effectiveness and efficiency of the method. [ABSTRACT FROM AUTHOR]

• A direct imaging method for recovering the elastic moment tensor point sources. • The numerical scheme is easy to implement, without any iteration or forward solver. • The imaging indicator is based on a special choice of the admissible frequencies. • Stability is analyzed and simulation examples are provided to validate the reconstructions. We investigate an inverse source problem of the time-harmonic elastic wave equation. Some novel sampling-type numerical schemes are proposed to identify the moment tensor point sources in the Lamé system from near-field measurements. Rigorous theoretical justifications are provided to show that the locations and moment tensors of the elastic sources can be uniquely determined from the multi-frequency displacement data. Several numerical examples are also presented to illustrate the validity and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

• Study a highly challenging inverse scattering with severe lack of information, which is new to the literature. • Propose a novel imaging scheme by incorporating physical insights into a machine learning method. • Extensive numerical results evidence the salient and highly promising features of the proposed method. • The new perspective should be able to develop novel schemes for tackling other inverse problems that cannot be tackled by traditional methods. In this paper, we consider artificial neural networks for inverse scattering problems. As a working model, we consider the inverse problem of recovering a scattering object from the (possibly) limited-aperture radar cross section (RCS) data collected corresponding to a single incident field. This nonlinear and ill-posed inverse problem is practically important and highly challenging due to the severe lack of information. From a geometrical and physical point of view, the low-frequency data should be able to resolve the unique identifiability issue, but meanwhile lose the resolution. On the other hand, the machine learning can be used to break through the resolution limit. By combining the two perspectives, we develop a fully connected neural network (FCNN) for the inverse problem. Extensive numerical results show that the proposed method can produce stunning reconstructions. The proposed strategy can be extended to tackling other inverse scattering problems with limited measurement information. [ABSTRACT FROM AUTHOR]