Relevance vector machine technique for the inverse scattering problem

A novel method based on the relevance vector machine（RVM） for the inverse scattering problem is presented in this paper.The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered.The nonlinearity is embodied in the relation between the scattered field and the target property,which can be obtained through the RVM training process.Besides,rather than utilizing regularization,the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output.Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy,convergence,robustness,generalization,and improved performance in terms of sparse property in comparison with the support vector machine（SVM） based approach.

A Regularized Newton Method in Inverse Scattering Problem from Cavities

We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization. For its approximate solution we propose a regularized Newton iteration scheme. For a foundation of Newton type methods we establish the Fr^chet differentiability of solution to the scattering problem with respect to the boundary of the cavity. Some numerical examples of the feasibility of the method are presented.

Inverse Electromagnetic Scattering by a Penetrable Chiral Object

We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.

Factorization method for inverse obstacle scattering problem in three-dimensional planar acoustic waveguides

In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.

A Method for Solving the Inverse Scattering Problem for Shape and Impedance of Crack

The inverse problem considered in this paper is to determine the shape and the impedance of crack from a knowledge of the time-harmonic incident field and the corresponding far field pattern of the scattered waves in two-dimension.The combined single-and double-layer potential is used to approach the scattered waves.As an important feature,this method does not require the solution of u and δu/δv at each iteration.An approximate method is presented and the convergence of this method is proven.Numerical examples are given to show that this method is both accurate and simple to use.

INVERSE SCATTERING PROBLEM FOR ONE-DIMENSIONAL SCHRDINGER OPERATORS RELATED TO THE GENERAL STARK EFFECT

This paper disccusses the inverse scattering problem for one-dimensional Schrodinger operatorsrelated to the general Stark effect. We provide a ganeral framework which can be applied both to theStark-effect operator and the ordinary Schrodinger operator.

Comparisons between Isotropic and Anisotropic TV Regularizations in Inverse Acoustic Scattering

This article compares the isotropic and anisotropic TV regularizations used in inverse acoustic scattering. It is observed that compared with the traditional Tikhonov regularization, isotropic and anisotropic TV regularizations perform better in the sense of edge preserving. While anisotropic TV regularization will cause distortions along axes. To minimize the energy function with isotropic and anisotropic regularization terms, we use split Bregman scheme. We do several 2D numerical experiments to validate the above arguments.

Microwave Through Wall Imaging via An Induced Current Learning Method

In this paper,an induced current learning method(ICLM)for microwave through wall imaging(TWI),named as TWI-ICLM,is proposed.In the inversion of induced current,the unknown object along with the enclosed walls are treated as a combination of scatterers.Firstly,a non-iterative method called distorted-Born backpropagation(DB-BP)is utilized to generate the initial result.In the training stage,several convolutional neural networks(CNNs)are cascaded to improve the estimated induced current.In addition,a hybrid loss function consisting of the induced current error and the permittivity error is used to optimize the network parameters.Finally,the relative permittivity images are conducted analytically using the predicted current based on ICLM.Both the numerical and experimental TWI tests prove that,the proposed method can achieve better imaging accuracy compared to traditional distorted-Born iterative method(DBIM).

DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES

In this paper we consider a kind of exterior transmission problem in which the refractive index n（x） is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions.

Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far-Field Data

Based on Broad Learning System with preprocessing,the impenetrable obstacles were reconstructed.Firstly,the far-field data were preprocessed by Random Forest,and the shapes of the obstacles were classified by dividing the far-field data into different categories.Secondly,the broad learning system was employed for reconstructing the unknown scatterer.The far-field data of the scatterer were regarded as the input nodes of mapped features in the network,and all the mapped features were connected with the enhancement nodes of random weights to the output layer.Subsequently,the coefficient of the output can be obtained by the pseudoinverse.This method for the recovery of the scattering obstacles is named RF-BLS.Finally,numerical experiments revealed that the proposed method is effective,and that the training speed was significantly improved,compared with the deep learning method.

THE FACTORIZATION METHOD FOR AN OPEN ARC

We consider the inverse scattering problem of determining the shape of a thin dielectric infinite cylinder having an open arc as cross section. Assuming that the electric field is polarized in the TM mode, this leads to a mixed boundary value problem for the Helmholtz equation defined in the exterior of an open arc in R2. We suppose that the arc has mixed Dirichlet impedance boundary condition, and try to recover the shape of the arc through the far field pattern by using the factorization method. However, we are not able to apply the basic theorem introduced by Kirsch to treat the far field operator F, and some auxiliary operators have to be considered. The theoretical validation of the factorization method to our problem is given in this paper, and some numerical results are presented to show the viability of our method.

THE RECONSTRUCTION OF OBSTACLES IN A WAVEGUIDE USING FINITE ELEMENTS

This paper concerns the reconstruction of a penetrable obstacle embedded in a waveg- uide using the scattered data due to point sources, which is formulated as an optimization problem. We propose a fast reconstruction method based on a carefully designed finite element scheme for the direct scattering problem. The method has several merits： 1） the linear sampling method is used to quickly obtain a good initial guess; 2） finite Fourier series are used to approximate the boundary of the obstacle, which is decoupled from the boundary used by the finite element method; and 3） the mesh is fixed and hence the stiff- ness matrix, mass matrix, and right hand side are assembled once and only minor changes are made at each iteration. The effectiveness of the proposed method is demonstrated by numerical examples.

Study of extracting characteristic parameters from a blood vessel

A geometrical acoustical method was used to describe the scattered ficld of a softtube (simulating a blood vessel). Inverse scattering problem of the soft-tube in the space domain and frequency domain was discussed. The scattered field was measured and the internal radius, external radius, velocity, density and attenuahon coefficient of the tube were reconstructed. The relative deviations were less than 5 %.

Simultaneous Scatterer Shape Estimation and Partial Aperture Far-Field Pattern Denoising

We study the inverse problem of recovering the scatterer shape from the far-field pattern(FFP)in the presence of noise.Furthermore,only a discrete partial aperture is usually known.This problem is ill-posed and is frequently addressed using regularization.Instead,we propose to use a direct approach denoising the FFP using a filtering technique.The effectiveness of the technique is studied on a scatterer with the shape of the ellipse with a tower.The forward scattering problem is solved using the finite element method(FEM).The numerical FFP is additionally corrupted by Gaussian noise.The shape parameters are found based on a least-square error estimator.If eu¥is a perturbation of the FFP then we attempt to find G,the scatterer shape,which minimizes k u¥−eu¥k using the conjugate gradient method for the denoised FFP.