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.

The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrdinger Equations

This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported potentials.For purpose of reconstructing the support of the potential,we derive a factorization of the scattering amplitude operator A and prove that the ranges of （A＊ A） ^1/4 and G which maps more general incident fields than plane waves into the scattering amplitude coincide.As an application we characterize the support of the potential using only the spectral data of the operator A.

Propagation modeling of ocean-scattered low-elevation GPS signals for maritime tropospheric duct inversion

The maritime tropospheric duct is a low-altitude anomalous refractivity structure over the ocean surface,and it can significantly affect the performance of many shore-based/shipboard radar and communication systems.We propose the idea that maritime tropospheric ducts can be retrieved from ocean forward-scattered low-elevation global positioning system（GPS） signals.Retrieval is accomplished by matching the measured power patterns of the signals to those predicted by the forward propagation model as a function of the modified refractivity profile.On the basis of a parabolic equation method and bistatic radar equation,we develop such a forward model for computing the trapped propagation characteristics of an ocean forward-scattered GPS signal within a tropospheric duct.A new GPS scattering initial field is defined for this model to start the propagation modeling.A preliminary test on the performance of this model is conducted using measured data obtained from a 2009-experiment in the South China Sea.Results demonstrate that this model can predict GPS propagation characteristics within maritime tropospheric ducts and serve as a forward model for duct inversion.

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.

~ Transform Demonstration of Dark Soliton Solutions Found by Inverse Scattering

One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.

Demonstration of Inverse Scattering Transform for DNLS Equation

Since the Jost solutions of the DNLS equation does not tend to the free Jost solutioins as ｜λ｜→∞, the usual inverse scattering transform （IST） must be revised. Beside the Kaup and Newell＇s approach, we propose a simple revision in constructing the equations of IST, where the usual Zakharov-Shabat kern is revised by multiplying λ^-2 or λ^-1. To justify the revision we show that the Jost solutions obtained do satisfy the pair of compatibility equations.

Solving Non-Isospectral mKdV Equation and Sine-Gordon Equation Hierarchies with Self-Consistent Sources via Inverse Scattering Transform

N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources andthe hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scatteringtransform.

Precisely quantifying bulk transition metal valence evolution in conventional battery electrode by inverse partial fluorescence yield

Precisely quantifying transition metal(TM) redox in bulk is a key to understand the fundamental of optimizing cathode materials in secondary batteries. At present, the commonly used methods to probe TM redox are hard X-ray absorption spectroscopy(hXAS) and soft X-ray absorption spectroscopy(sXAS).However, they are both facing challenges to precisely quantify the valence states of some transition metals such as Mn. In this paper, Mn-L iPFY(inverse partial fluorescence yield) spectra extracted from Mn-L m RIXS(mapping of resonant inelastic X-ray scattering) is adopted to quantify Mn valence states. Mn-L i PFY spectra has been considered as a bulk-sensitive, non-distorted probe of TM valence states.However, the exact precision of this method is still unclear in quantifying practical battery electrodes.Herein, a series of LiMn_(2)O_(4) electrodes with different charge and discharge states are prepared. Based on their electrochemical capacity(generally considered to be very precise), the precision of Mn iPFY in quantifying bulk Mn valence state is confirmed, and the error range is unraveled. Mn-L mRIXS iPFY thus is identified as one of the best methods to quantify the bulk Mn valence state comparing with hXAS and sXAS.

INVERSE PROBLEM FOR THE VISCOELASTIC MEDIUM WITH DISCONTINUOUS WAVE IMPEDANCE

In this paper, the inverse problem for the viscoelastic medium is investigated in the time domain, in which the wave impedance of the medium is discontinuous at the rear interface. The differentio-integral equations governing the behavior of the scattering and propagation operators are utilized to reconstruct the relaxation modulus of the viscoelastic medium. A new approach, in which only the one-side measurement reflection data for one round trip through the viscoelastic layer, is developed. The numerical examples are given at the end of the paper. Ir is shown that the curves of the reconstructed moduli coincide very well with the original relaxation moduli.

LINEARIZED INVERSE SCATTERING FOR ELASTIC PARAMETERS IN A HALF-SPACE WITH REFLECTION DATA

The multi-parameter inversion of elastic wave equation in a half-space within the Born approximation is studied. A method of simultaneously reconstructing the configurations of the density and Lame parameters of the medium was presented by use of a wideband measuring schemes in which transmitters and receivers scan over the half-space surface. It is shown that the reflected waves generated by horizontal and vertical pulses on the surface can be decomposed into P-->P, P-->S, S-->P and S-->S types of scattering components. As is expected, these components contain enough information for desired restruction. From them the density and two Lame parameters are determined explicitly, and the results obtained have the form of filtered back-propagation as in the acoustic diffraction tomography.

An Improved Hybrid Method for Inverse Obstacle Scattering Problems

An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method.

Seismic inversion with generalized Radon transform based on local second-order approximation of scattered field in acoustic media

Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms （Born/ single scattering approximation） are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation （heterogeneous） medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps： firstly, to handle the forward scattering by taking into account the second- order Born approximation, which is related to generalized Radon transform （GRT） about quadratic scattering poten- tial; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation （3c/c0） of background media up to 10 %, andits inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the per- turbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a trans- mission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process.

基于改进Morozov偏差原理的动态光散射粒度反演

与窄粒度分布反演相比,宽粒度分布的反演难以获取与其相适应的正则参数。为提高宽分布颗粒体系反演结果的准确性,提出基于改进Morozov偏差原理,通过遗传算法迭代求取正则参数的方法,该方法通过小波包分解求出电场自相关函数的噪声分量,利用Morozov偏差原理建立适应值函数,在正则参数经验范围内生成初始种群,将适应值函数与初始种群带入遗传算法,全局寻找最优适应值对应的参数值作为正则参数。模拟与实测数据的反演结果表明,在窄分布颗粒体系条件下,所提方法与L-curve准则反演结果无显著差异,在宽分布条件下,所提方法反演结果的性能指标均优于L-curve准则,且避免了宽粒度分布条件下可能出现的虚假峰情况,表现出明显优于L-curve准则的宽分布反演效果。

Inverse scattering method and soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields

A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.

Demonstration of Inverse Scattering Transform in G-L-M Formalism for NLS Equation in Normal Dispersion with Non-vanishing Boundary

Using the integral representation of the Jost solution,we deduce some conditions as the kernel functionN(x,y,t)if the Jost solution satisfies the two Lax equations.Then we verify the multi-soliton solution of NLS equationwith non-vanishing boundary conditions if we prove that these conditions can be demonstrated by the GLM equation,which determines the kernel function N(x,y,t)in according to the inverse scattering method.

Full waveform inversion based on hybrid gradient

The low-wavenumber components in the gradient of full waveform inversion(FWI)play a vital role in the stability of the inversion.However,when FWI is implemented in some high frequencies and current models are not far away from the real velocity model,an excessive number of low-wavenumber components in the gradient will also reduce the convergence rate and inversion accuracy.To solve this problem,this paper firstly derives a formula of scattering angle weighted gradient in FWI,then proposes a hybrid gradient.The hybrid gradient combines the conventional gradient of FWI with the scattering angle weighted gradient in each inversion frequency band based on an empirical formula derived herein.Using weighted hybrid mode,we can retain some low-wavenumber components in the initial lowfrequency inversion to ensure the stability of the inversion,and use more high-wavenumber components in the high-frequency inversion to improve the convergence rate.The results of synthetic data experiment demonstrate that compared to the conventional FWI,the FWI based on the proposed hybrid gradient can effectively reduce the low-wavenumber components in the gradient under the premise of ensuring inversion stability.It also greatly enhances the convergence rate and inversion accuracy,especially in the deep part of the model.And the field marine seismic data experiment also illustrates that the FWI based on hybrid gradient(HGFWI)has good stability and adaptability.

A Deep Learning Method to Process Scattered Field Data in Biomedical Imaging System

This paper proposed a deep-learning-based method to process the scattered field data of transmitting antenna,which is unmeasurable in inverse scattering system because the transmitting and receiving antennas are multiplexed.A U-net convolutional neural network(CNN)is used to recover the scattered field data of each transmitting antenna.The numerical results proved that the proposed method can complete the scattered field data at the transmitting antenna which is unable to measure in the actual experiment and can also eliminate the reconstructed error caused by the loss of scattered field data.

Collision off-axis position dependence of relativistic nonlinear Thomson inverse scattering of an excited electron in a tightly focused circular polarized laser pulse

This paper presents a novel view of the impact of electron collision off-axis positions on the dynamic properties and relativistic nonlinear Thomson inverse scattering of excited electrons within tightly focused, circularly polarized laser pulses of varying intensities. We examine the effects of the transverse ponderomotive force, specifically how the deviation angle and speed of electron motion are affected by the initial off-axis position of the electron and the peak amplitude of the laser pulse. When the laser pulse intensity is low, an increase in the electron's initial off-axis distance results in reduced spatial radiation power, improved collimation, super-continuum phenomena generation, red-shifting of the spectrum's harmonic peak, and significant symmetry in the radiation radial direction. However, in contradiction to conventional understandings,when the laser pulse intensity is relatively high, the properties of the relativistic nonlinear Thomson inverse scattering of the electron deviate from the central axis, changing direction in opposition to the aforementioned effects. After reaching a peak, these properties then shift again, aligning with the previous direction. The complex interplay of these effects suggests a greater nuance and intricacy in the relationship between laser pulse intensity, electron position, and scattering properties than previously thought.

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.