In this paper, the generalized multiple measurement vectors (GMMV) linear inversion method is applied to the reconstruction of the 3-D Fresnel data, provided by the Institue Fresnel (Marseille, France). The results show that the GMMV-based method can obtain good resolution along the x- and y- axes, while poor resolution along the z-axis, because there were only receiving antennas distributed on the x-o-y plane, indicating that the diversity of the measurement angle is critical for the GMMV method. ... Read more

In this paper, a linear model based on multiple measurement vectors' model is proposed to formulate the inverse scattering problem of highly conductive objects at one single frequency. Considering the induced currents that are mostly distributed on the boundaries of the scatterers, joint sparse structure is enforced by a sum-of-norm regularization. Since no a priori information is required and no approximation of the scattering model has been made, the proposed method is versatile. Imaging results with transverse magnetic and transverse electric polarized synthetic data and Fresnel data demonstrate its higher resolving ability than both linear sampling method and its improved version with higher, but acceptable, computational complexity. ... Read more

The linear shape reconstruction method based on the generalized multiple measurement vectors model is a newly proposed approach which is able to effectively retrieve the morphological information of dielectric/metallic scatterers with competitive imaging resolution. In this letter, we have extended this approach to quantitative inversion, and the proposed approach turns out to be effective even for complicated scatterers and highly efficient in comparison to nonlinear iterative methods. The inverted results obtained by processing the transverse magnetic polarized Fresnel data-sets of the year 2005 demonstrate the validity of the proposed method in real applications. ... Read more

In this paper, a novel linear method for shape reconstruction is proposed based on the generalized multiple measurement vectors (GMMV) model. Finite difference frequency domain (FDFD) is applied to discretized Maxwell’s equations, and the contrast sources are solved iteratively by exploiting the joint sparsity as a regularized constraint. Cross validation (CV) technique is used to terminate the iterations, such that the required estimation of the noise level is circumvented. The validity is demonstrated with an excitation of transverse magnetic (TM) experimental data, and it is observed that, in the aspect of focusing performance, the GMMV-based linear method outperforms the extensively used linear sampling method (LSM). ... Read more

Cross-correlated contrast source inversion (CC-CSI) is a nonlinear iterative inversion method that is proposed recently for solving the inverse scattering problems. In CC-CSI, a cross-correlated error is constructed and introduced to the cost functional, which improves the inversion ability when compared to the classical design of the cost functional by exploiting the mismatch between the data error and state error. In this paper, the multifrequency inversion for electromagnetic waves is considered and a multifrequency version of CC-CSI is proposed. Numerical and experimental inversion results of both transverse magnetic and transverse electric polarization demonstrate that when multifrequency data are available, CC-CSI still outperforms the multiplicative-regularized CSI method in the inversion of more complicated scatterers. ... Read more

One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse scattering problem is put into a discretized finite-difference frequency-domain scheme and linearized into a cascade of two linear functionals. To deal with the nonuniqueness effectively, the joint structure of the contrast sources is exploited using a sum-of- ℓ1 -norm optimization scheme. A cross-validation technique is used to check whether the optimization process is accurate enough. The total fields are, then, calculated and used to reconstruct the contrast by minimizing a cost functional defined as the sum of the data error and the state error. In this procedure, the total fields in the inversion domain are computed only once, while the quality and the accuracy of the obtained reconstructions are maintained. The novel method is applied to ground-penetrating radar imaging and through-the-wall imaging, in which the validity and the efficiency of the method are demonstrated. ... Read more

In this paper, we improved the performance of the contrast source inversion (CSI) method by incorporating a so-called cross-correlated cost functional, which interrelates the state error and the data error in the measurement domain. The proposed method is referred to as the cross-correlated CSI. It enables better robustness and higher inversion accuracy than both the classical CSI and multiplicative regularized CSI (MR-CSI). In addition, we show how the gradient of the modified cost functional can be calculated without significantly increasing the computational burden. The advantages of the proposed algorithms are demonstrated using a 2-D benchmark problem excited by a transverse magnetic wave as well as a transverse electric wave, respectively, in comparison with classical CSI and MR-CSI. ... Read more

The inverse scattering problem is inherently nonlinear and improperly posed. Relevant study, such as the existence and uniqueness of the solution, the completeness of the far field pattern, etc., involves an abstruse mathematical theory. In our daily life, the inversion techniques play a significant role in areas such as radar, sonar, geophysical exploration, medical imaging and nondestructive testing. This thesis is focused on the qualitative and quantitative reconstruction of shape and medium parameters of scattering objects in electromagnetic inverse scattering theory. The major contributions of this thesis are 1) the proposal of a novel cross-correlated error termand 2) the proposal of the sum-of-normregularized reconstruction algorithm. The significance of the former lies in the fact that the proposed error term fills up a gap hidden in the classical “state error Å data error” cost functional. In the optimization approaches, the data error term tends to recover the unknown properties of the objects directly from the measurement data, while the state error term attempts to ensure that the recovered results satisfy Maxwell’s equations in the field domain. In other words, the solution must behave well in both the measurement domain and the field domain. However, there is still a gap in between because the minor mismatch in the field domain is not monitored in the measurement domain. The proposed crosscorrelated error is a constraint which tends to get the mismatch in the field domain under control in the measurement domain. Therefore, one can say that this novel error term revolutionizes the formulation of the minimization functional of inversion techniques based on optimization theory. The significance of the latter is that the proposed reconstruction scheme enables us to excavate the joint information hidden in the formulation of multiple inverse source problems, without any significant additional computational effort. Although the sum-of-norm regularization is not necessarily the best regularization constraint for some complicated scatterers, it demonstrates at least two points: 1) for an inverse source problem, benefits can be obtained from use of different incident fields; 2) the sum-of-norm regularization brings better resolving ability due to the joint processing of the multiple contrast source vectors. The research results in this thesis are also applicable to the acoustic inverse scattering problems. Application of the qualitative and quantitative reconstruction approaches developed in this thesis to the experimental data in different areas of wave-field inversion would be very interesting as future work. ... Read more

This paper presents the application of the shape reconstruction method based on the generalized multiple measurement vectors (GMMV) model on the multi-frequency transverse magnetic (TM) and transverse electric (TE) polarized Fresnel data, measured by the Institue Fresnel (Marseille, France) from cylindrical objects. Finite difference frequency domain (FDFD) is applied to discretize the Maxwell's equations, and the contrast sources are solved iteratively by exploiting the joint sparsity as a regularized constraint. Cross validation (CV) technique is used to terminate the iterations and give the estimation of the noise level at the same time. The results show that the GMMV-based linear method successfully performs shape reconstruction of a large variety of scatterers. ... Read more

In this paper, 3D imaging of forward-looking Ground Penetrating Radar (GPR) data acquired by rotating antennas have been done. The data acquisition procedure mimics data collection of the Tunnel Boring Machine (TBM). Real GPR data for a Karst scenario were analyzed, preprocessed and finally imaged with back-projection method. Results show that objects buried in the subsurface of the ground can be successfully imaged using rotating antennas, which is a solid foundation for further development of the GPR system on TBM. ... Read more

In this paper, the nonlinear perfect electric conductor (PEC) inverse scattering problem was addressed with a linear model. First, finite difference frequency domain (FDFD) was used to discretize the problem. Then, the contrast and the total field were included into the contrast source to formulate a linear model. Due to the fact that the induced current only exists
on the surface of the PEC scatterers, reconstruction methods in compressive sensing (CS) can be used to recover the contrast source which is able to indicate the shape of the PEC objects. To further enhance the inversion performance, the multiple measurement vector (MMV) model was used to exploit the joint sparsity of the contrast sources corresponding to different incident angles. This method shares some common merits with other inversion methods: First, it does not require a priori information on the position and quantity of the scatterers. Second, nonconvex PEC objects can be successfully reconstructed. Third, it enables simple incorporation with complicated background media without increasing extra computational burden. In addition, it also shows its own advantages that cannot be achieved in other inversion methods: First, it solves the nonlinear inverse scattering problems based on the vectorial Maxwell equations with a linear model.
Second, the sensing matrix is much less compared to the inverse of the stiffness matrix in FDFD scheme, so it can be computed and stored beforehand to circumvent the matrix inverse computation and achieve fast inversion. Numerical simulation results with the transverse magnetic (TM) data in 2D configuration demonstrated the validity of the proposed method. ... Read more

In this paper, a generalized electromagnetic (EM) wave penetrating propagation model is presented to improve the imaging quality for through-the-wall radar with compressed sensing (CS) technique,. Compared with those penetrating propagation models established only in the 2-D space, the proposed model considers the propagation path in the 3-D space to reduce the mismatch error between the observation model used in CS and the physical procedure. The EW wave propagation path is calculated with an analytical expression with some approximation for stand-off sensing, which is computationally efficient for CS imaging. Real data are used to validate the model proposed. It is shown that the CS imaging with the model proposed can yield better performance in locating and clutter suppression. ... Read more