The radar imaging method, based on matched filtering (MF), generates high gratings and sidelobes in sparse aperture data, resulting in artifacts in the radar image. The theory of compressive sensing (CS) has brought a breaking change to radar imaging, and imaging enhancement can be realized by exploiting the sparsity of the target image. However, traditional sparse imaging methods ignore the correlation between scatterers. This leads to difficulties in accurately extracting the target’s shape contour and structural features. Thus, in this paper, a convolutional reweighted model based on structured sparsity features is proposed. Specifically, a dynamically relaxing threshold is achieved through the convolutional reweightedl1norm, promoting the sparsity of clustered structures in radar images. Furthermore, to avoid large-scale matrix inversion, the issue is respectively addressed through the alternating direction method of multipliers (ADMM) joint gradient descent framework and linearization approximation approach. In addition, the priori information of MF is utilized to adaptively update the imaging support set during the iteration process, aiming to reduce the data storage pressure. Finally, a large number of simulation and experimental results confirm the generality of the proposed algorithms for radar data in different frequency bands, as well as their superiority in terms of computational efficiency and image quality.

A sparse planar array often suffers from the strong grating-lobes that deteriorate inversion performance due to spatial undersampling. In the paper, a diffraction tomography (DT) algorithm is proposed to solve three-dimensional (3-D) electromagnetic inverse scattering problems with a sparse planar array and polarization diversity. The method deals with multifrequency multipolarization data as follows: firstly, doing a polarization fusion; next, using the exact coordinate transformation; then decoupling and modifying the aliased multifrequency spatial spectrum of the permittivity and the conductivity; finally, applying the range-normalization two-dimensional coherence factor (2-D CF) weighting. The weak scatterers’ geometries and dielectric properties can be well reconstructed under low-contrast conditions, and the non-weak scatterers can also be detected. The proposed method outperforms the conventional DT approach regarding grating-lobes and noise suppression without compromising quantitative inversion performance, as demonstrated by the inverted results obtained from synthetic and experimental data.

In this paper, a modified singular value decomposition (SVD) method for quantitative inversion of the weak scatterers with multi-frequency data is presented. The proposed method can utilize the low frequency information content effectively and obtain the permittivity and the conductivity simultaneously. Meanwhile, multi-frequency configurations based on the equal wavelength interval and the equal frequency interval are discussed for more accurate inversion. The modified SVD is proposed by firstly reconstructing the scattered field and the operator, then decoupling the permittivity and conductivity, and finally mapping the scattered field to the contrast function. Inversion results with synthetic data demonstrate that the proposed method outperforms the conventional SVD approach in terms of quantitative inversion accuracy for weak scatterers of the multi-frequency data.

Without phase information of the measured field data, the design complexity of the observation equipment can be greatly simplified. In the meantime, the phaseless data inverse scattering problems counter more serious nonlinearity and ill-posedness compared to the full data ones. In this article, a multifrequency cross-correlated contrast source inversion (CSI) method using phaseless measurements of the total fields (referred to as PD-CC-CSI) is proposed. By introducing the cross-correlated error term to the cost functional, PD-CC-CSI shows better robustness against data noise and challenges in more complicated inversion scenarios. Inverted results with transversal magnetic (TM) polarized synthetic and experimental data demonstrate the advantages of PD-CC-CSI in comparison to the phaseless data CSI (PD-CSI) method and its variant PD-MR-CSI. In addition, an empirical approach has been proposed to effectively determine the optimal inverted results. Since a fast algorithm can be straightforwardly applied, phaseless inversion with multifrequency data can be done within a few minutes.

Diffraction tomography (DT) is a linear approach to solving electromagnetic inverse scattering problems. Based on the weak scattering assumptions (such as Born or Rytov approximations), the spatial spectrum of the contrast at one certain frequency is a linear mapping of the scattered field data. As is well known, using more frequencies means better performance of noise suppression. However, the spatial spectra are aliased in cases of multi-frequency data. In addition, the permittivity and the conductivity are coupled in the aliased multi-frequency spatial spectrum. In this paper, a quantitative DT for weak scatterers is proposed by firstly doing a coordinate transformation, then decoupling the permittivity and the conductivity, and finally modifying the aliased multi-frequency spatial spectrum. In doing so, the modified spatial spectra of the permittivity and conductivity are formulated respectively, leading to a quantitative diffraction tomography for weak scatterers based on aliasing modification of the multi-frequency spectrum. Inversion results with synthetic and experimental data demonstrate that the proposed method outperforms the conventional DT approach in terms of quantitative inversion accuracy for weak scatterers of multi-frequency data while maintaining the anti-noise performance.

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.

Soon after its innovation, compressive sensing (CS) was rapidly applied to radar imaging. However, the huge computational complexity and the memory requirements have become the bottlenecks in its widespread applications to large-scale and real-time radar imaging. In this paper, two novel methods based on fast Gaussian gridding nonuniform fast Fourier transform are proposed to speed up CS radar imaging and reduce the memory requirement. By using the proposed methods, the application of CS imaging method can be extended to large-scale and real-time radar imaging with high reconstructing efficiency and small memory requirement. Theoretical analysis and numerical results from the aspects of accuracy, efficiency, and memory requirement validate the proposed methods. Simulation and real data imaging results by spectral projection gradient ℓ1-norm method are given to further demonstrate the efficiency of the proposed methods.