Nonlinear Inverse Scattering Research Articles

Applications of Non-linear Inverse Compton Scattering based on the Laser Plasma Accelerators

The generation of energetic photons in the context of inverse Compton scattering has attracted a great lot of interest from many contemporary scientific fields. Radiobiology, materials physics, and medicine are some of the current fields where inverse Compton scattering is used. In this study, the applications of nonlinear inverse Compton scattering will be demonstrated and illustrated based on laser plasma interaction. This paper introduces and highlights the current advancement in this area, which is a crucial component of quantum physics, as well as the potential uses in the future depending on additional study. Thorough explanations are demonstrated and talked about the uses of inverse Compton scattering. To highlight our thoughts on present developments and potential future advancements in the field, we have extended and expanded on the theme using simulations and experimental data. These results pave a path to generate and shed light on guiding further state-of-art proposals for High flux X/gamma ray generation.

Group Sparsity Penalized Contrast Source Solution Method for 2-D Non-Linear Inverse Scattering

A group sparsity penalized CSI in the wavelet domain is proposed to alleviate ill-posedness within the framework of a contrast-source inversion (CSI) method. It is then applied to the retrieval of a large inhomogeneous dielectric scatterer from time-harmonic single-frequency data. As dependency exists between wavelet coefficients at different scales, referred to as the parent-child relationship, it enables to yield the wavelet quad tree structure. Therefore, wavelet coefficients can be regarded not only as pixel-wise sparse, but also group-wise sparse. Focus is put on using the dual-tree complex wavelet transform ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {C}$ </tex-math></inline-formula> WT) to properly achieve the sought-after group-wise sparse representation of the spatial distribution of the contrast. It provides a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> norm which is added to the standard cost functional to enforce group sparsity onto the wavelet coefficients of the spatially-varying contrast. The replication strategy is combined with the proximal method in order to solve the overlapping group penalized problem. Simulations from synthetic data in different configurations with in particular different signal-to-noise ratios illustrate pros and cons of the proposed method. The approach is shown to overcome the standard CSI method in demanding situations. Comparisons with the discrete wavelet transform (DWT) as usually performed and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> norm confirm the advantage of the proposed methodology.

A New Scheme for Solving Highly Nonlinear Inverse Scattering Problems With Noise Disturbance

A New Scheme for Solving Highly Nonlinear Inverse Scattering Problems With Noise Disturbance

On Phase Information for Deep Neural Networks to Solve Full-Wave Nonlinear Inverse Scattering Problems

The phase information's role in deep neural networks (DNNs) to solve the electromagnetic inverse scattering problems is investigated. The feedforward neutral network model with complex-valued (CV) data stream and the corresponding CV backpropagation training algorithm are proposed to realize CV convolutional neural networks. Numerical examples are carried out to demonstrate the phase information's role in DNNs in terms of generalization capability as well as the convergence speed in the training stage.

Low-Frequency Data Prediction With Iterative Learning for Highly Nonlinear Inverse Scattering Problems

In this work, we present a deep-learning-based low-frequency (LF) data prediction scheme to solve the highly nonlinear inverse scattering problem (ISP) with strong scatterers. The nonlinearity of ISP is alleviated by introducing the LF components in full-wave inversion. In this scheme, a deep neural network (DNN) is trained to predict the absent LF scattered field data from the measured high-frequency (HF) data. Then, a frequency-hopping technique is applied to invert the predicted LF data and measured HF data, where the inverted LF model is served as an initial guess for the HF data inversion. In this way, the risk of HF data inversion getting trapped in local minima is largely reduced. Furthermore, an iterative training method is employed to continuously update the DNN based on the previous inverted model to predict more accurate LF data, thereby improving the reconstruction result. Both synthetic and experimental results are performed to verify the efficacy of this scheme.

Quantitative Non-Linear Inverse Scattering: A Wealth of Possibilities Through Smart Rewritings of the Basic Equations

Nonlinearity arising from mutual interactions is one of the two main difficulties to be addressed in inverse scattering. In this paper, we review and describe under a common rationale some approaches which have been introduced in literature in order to counteract nonlinearity. In particular, we focus on possible rewritings of the Lippman Schwinger basic equation such to reduce the degree of nonlinearity of inverse scattering problem. In detail, three different rewritings are discussed and compared by emphasizing similarities and the differences, and in the same rewriting spirit, we also summarize and discuss the Virtual Experiments framework. Then, some possible joint exploitations of the above concepts are introduced, discussed and tested against numerical examples.

Accelerating Uncertainty Quantification for Nonlinear Inverse Scattering Problems With High Contrast Media by Direct Envelope Methods and Krylov Subspace Iterative Integral Equation Solvers

Uncertainty quantification related to nonlinear inverse scattering problems often involves the posterior covariance matrix that cannot be effectively estimated but still need to be considered as an important part of the nonlinear inverse scattering problem. The objective of this work is to show how to take advantage of a Bayesian framework to estimate the uncertainty of velocity reconstruction in the nonlinear inverse scattering imaging. The key ingredients are twofold. On the one hand, we rely on a Kalman Filter method, equipped with an optimization scheme, to solve the inverse problem. We use the distorted Born iterative method to formulate the sensitivity kernel. It directly uses an explicit representation of the data sensitivity function in terms of Green functions, rather than the indirect optimization approach based on the adjoint state method, in which the Green’s functions are based on integral equations. On the other hand, we use the direct envelope methods to provide the initial guess (large-scale smooth model) to overcome the nonlinearity in the inverse scattering problems. We first investigate the uncertainty of velocity imaging in high contrast media. Then we show by means of Lippmann-Schwinger-type equations that the uncertainty of multiparameter inverse scattering problems can be addressed. Numerical results dealing with the uncertainty of nonlinear inverse scattering problems in the case of both isotropic and anisotropic media highlight the important role played by uncertainty quantification.

Wavelet-Based Subspace Regularization for Solving Highly Nonlinear Inverse Scattering Problems with Contraction Integral Equation

A wavelet transform twofold subspace-based optimization method (WT-TSOM) is proposed to solve the highly nonlinear inverse scattering problems with contraction integral equation for inversion (CIE-I). While the CIE-I is able to suppress the multiple scattering effects within inversion (without compromising the accuracy of the physics), proper regularization is needed. In this paper, we investigate a new type subspace regularization technique based on wavelet expansions for the induced currents. We found that the bior3.5 wavelet is a good choice to stabilize the inversions with the CIE-I model and in the meanwhile it also can rectify the contrast profile. Numerical tests against both synthetic and experimental data show that WT-TSOM is a promising regularization technique for inversion with CIE-I.

Integral Equation Methods With Multiple Scattering and Gaussian Beams in Inhomogeneous Background Media for Solving Nonlinear Inverse Scattering Problems

I develop inverse scattering methods for velocity reconstruction in the subsurface, based on multiple scattering theory, Gaussian beams and nonlinear Born approximation. This method is based on a new version of the distorted Born iterative inverse scattering method. It directly uses an explicit representation of the data sensitivity function in terms of Green functions, rather than the indirect optimization approach based on the adjoint state method. I propose three direct scattering methods for forward modeling, namely, Gaussian beam integral equation propagators, nonlinear Born approximation, and multiple scattering. First, I apply a sensitivity kernel incorporating the Gaussian beam summation-based integral equation method and compute the background medium Green's function in an inhomogeneous medium. Then I extend an approximate solution of the Lippmann-Schwinger equation, referred to as nonlinear Born approximation to inverse scattering problem. I apply the nonlinear Born approximation to forward modeling at each iteration. Furthermore, I combine the Gaussian beams with the multiple scattering theory for nonlinear scattering problems. I obtain the inversion results using the proposed approaches, which shows the capability for inverse scattering imaging. I have carried out several numerical experiments that involve reconstructing the resampled Marmousi and Society of Exploration Geophysicists (SEG)/European Association of Geoscientists and Engineers (EAGE) salt models from its smoothed version.

A Multiresolution Contraction Integral Equation Method for Solving Highly Nonlinear Inverse Scattering Problems

The solution of highly nonlinear inverse scattering problems is addressed. An innovative multiresolution microwave imaging technique, which leverages on the profitable integration of the contraction integral equation for inversion (CIE-I) and the iterative multiscaling approach (IMSA), is proposed. Thanks to the joint exploitation of the features of the CIE-I formulation and the IMSA, the arising IMSA-CIE-I inversion technique provides faithful reconstructions of complex-shaped strong scatterers with enhanced resolution and computational efficiency with respect to the state-of-the-art competitive alternatives. Numerical and experimental test cases verify the effectiveness and limitations of the proposed method.

Solving Phaseless Highly Nonlinear Inverse Scattering Problems With Contraction Integral Equation for Inversion

At high frequencies, phase measurement is difficult to meet the accuracy required for imaging, and it is more susceptible to noise pollution. Consequently, it is important to develop inversion models and algorithms for electromagnetic inverse scattering problems with phaseless data (PD-ISPs). Compared to the ISPs with full-data (FD-ISPs), the PD-ISPs are more nonlinear due to the lack of the phase information. Aiming at solving highly nonlinear PD-ISPs, in this article we present a contraction integral equation for inversion (CIE-I) regularized with Fourier subspace via contrast source inversion method, denoted as PD-CSI-CIE-I. Under the model of CIE-I, the nonlinearity of PD-ISPs can be effectively alleviated. In order to stabilize CIE-I, a nested optimization scheme with multi-round procedure is adopted by choosing the proper number of low-frequency components from unknown induced current spanned in the Fourier subspace. By the Fourier bases expansion of induced current, the computational cost can be further reduced. Numerical and experimental examples validate the efficiency of the proposed inversion method. Futher, it is shown that the proposed PD-CSI-CIE-I has a stronger inversion capability than the one with the Lippmann-Schwinger integral equation (LSIE) when tackling high contrast scatterers with phaseless data.

Deep-Learning Schemes for Full-Wave Nonlinear Inverse Scattering Problems

This paper is devoted to solving a full-wave inverse scattering problem (ISP), which is aimed at retrieving permittivities of dielectric scatterers from the knowledge of measured scattering data. ISPs are highly nonlinear due to multiple scattering, and iterative algorithms with regularizations are often used to solve such problems. However, they are associated with heavy computational cost, and consequently, they are often time-consuming. This paper proposes the convolutional neural network (CNN) technique to solve full-wave ISPs. We introduce and compare three training schemes based on U-Net CNN, including direct inversion, backpropagation, and dominant current schemes (DCS). Several representative tests are carried out, including both synthetic and experimental data, to evaluate the performances of the proposed methods. It is demonstrated that the proposed DCS outperforms the other two schemes in terms of accuracy and is able to solve typical ISPs quickly within 1 s. The proposed deep-learning inversion scheme is promising in providing quantitative images in real time.

A Hybrid Regularization Technique for Solving Highly Nonlinear Inverse Scattering Problems

Solving inverse scattering problems (ISPs) for targets with high contrasts and/or large dimensions suffer from severe ill-posedness and strong nonlinearity. Recently, a family of new integral equations (NIE) has been proposed to tackle such problems, in which the multiple scattering effects in estimating contrasts during inversions are suppressed by the local wave effects. This effectively reduces the nonlinearity of ISPs by transforming the problems into a new form. As in most inversions, to achieve better (stabler and faster) inversion efficiency, proper regularization techniques are needed. This paper provides the detailed studies on the two different types of regularization techniques in the inversions with the NIE, i.e., the twofold subspace-based optimization method, directly applied in the modeling, and the total variation type multiplicative regularization, conventionally applied on the unknowns. We will show that how each regularization works with the NIE and how they work together with the NIE to obtain the better performance in terms of reducing the nonlinearity and increasing the stability of the inversions. Numerical tests against synthetic data and experimental data are provided to verify the interests.

Non-Linear Inverse Scattering via Sparsity Regularized Contrast Source Inversion

Two compressive sensing inspired approaches for the solution of non-linear inverse scattering problems are introduced and discussed. Differently from the sparsity promoting approaches proposed in most of the papers published in the literature, the two methods here tackle the problem in its full non-linearity, by adopting a contrast source inversion scheme. In the first approach, the ${\ell _1}$ -norm of the unknown is added as a weighted penalty term to the contrast source cost functional. The second, and (to the best of our knowledge) completely original, approach enforces sparsity by constraining the solution of the non-linear problem into a convex set defined by the ${\ell _1}$ -norm of the unknown. A numerical assessment against a widely used benchmark example (the “Austria” profile) is given to assess the capabilities of the proposed approaches. Notably, the two approaches can be applied to any kind of basis functions and they can successfully tackle both reduced number of data (with respect to Nyquist sampling) and/or overcomplete dictionaries.

3-D Nonlinear Acoustic Inverse Scattering: Algorithm and Quantitative Results.

We describe a novel 3-D ultrasound technology, the quantitative transmission ultrasound system and algorithm to image a pendent breast in a water bath. Quantitative accuracy is verified using phantoms. Morphological accuracy is verified using cadaveric breast and in vivo images, and spatial resolution is estimated. This paper generalizes an earlier 2-D algorithm to a full 3-D inversion algorithm and shows the importance of such a 3-D algorithm for artifact suppression as compared with the 2-D algorithm. The resultant high-resolution ultrasound images, along with quantitative information regarding tissue speed of sound/stiffness, provide a more accurate depiction of the breast anatomy and lesions, contributing to improved breast care.

Corrections to “An Algebraic Solution Method for Nonlinear Inverse Scattering”

We would like to correct a statement that we gave in our comments to [1, eq. (9)] . While such a change does not affect in any way the validity of the inversion approach presented in [1] and the results therein obtained, it is nevertheless important to discuss it, in order to provide the correct physical interpretation of (9).

A Recursive Born Approach to Nonlinear Inverse Scattering

The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails.

A New Integral Equation Method to Solve Highly Nonlinear Inverse Scattering Problems

A family of new integral equations (NIE) is proposed in this paper, which are transformed from the original Lippmann–Schwinger integral equation. It can be shown that the NIE can effectively reduce the nonlinearity of inverse scattering problems by reducing the global nonlinear effects, introduced by the multiple scattering behaviors, in estimating the contrast. Equipping the previously proposed twofold subspace-based optimization method with such NIE, the new inversion method is able to solve inverse scattering problems with strong scatterers, like with high contrast and/or large dimensions (in terms of wavelength) ones. Furthermore, such a family of NIE could provide a convenient tool to appraise reconstructed results. Several representative numerical tests are carried out, using both synthetic and experimental data, to verify the efficacy of the new inversion method.

A Methodology Based on Mesh Morphing Algorithm and Improved Tabu Algorithm for Non-linear Inverse Scattering

This paper proposed an inversion method, for the study of non-linear inverse scattering problems, which is derived from an improved tabu algorithm and a mesh morphing technique based on finite-element method. A remesh-free morphing method is reported to improve the quality of the reconstruction with neither remeshing nor increases in the number of unknowns. Refined meshes can be quickly derived using a coordinate mapping technique according to a given fine mesh and an initial coarse mesh. The sensitivity analysis is used as an indication of the step vector to help obtain the global optimum rapidly, thus the proposed methodology is particularly useful for time consuming inverse problems. Numerical results both in 2-D and 3-D examples are given to showcase the efficiency and effectiveness of the proposed method.

Buried Object Detection by an Inexact Newton Method Applied to Nonlinear Inverse Scattering

An approach to reconstruct buried objects is proposed. It is based on the integral equations of the electromagnetic inverse scattering problem, written in terms of the Green’s function for half-space geometries. The full nonlinearity of the problem is exploited in order to inspect strong scatterers. After discretization of the continuous model, the resulting equations are solved in a regularization sense by means of a two-step inexact Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations.