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.

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 reweighted l ₁ norm, 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.

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- $\ell _{1}$ -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.

Radar images suffer from the impact of sidelobes. Several sidelobe-suppressing methods including the convolutional neural network (CNN)-based one has been proposed. However, the point spread function (PSF) in the radar images is sometimes spatially variant and affects the performance of the CNN. We propose the spatial-variant convolutional neural network (SV-CNN) aimed at this problem. It will also perform well in other conditions when there are spatially variant features. The convolutional kernels of the CNN can detect motifs with some distinctive features and are invariant to the local position of the motifs. This makes the convolutional neural networks widely used in image processing fields such as image recognition, handwriting recognition, image super-resolution, and semantic segmentation. They also perform well in radar image enhancement. However, the local position invariant character might not be good for radar image enhancement, when features of motifs (also known as the point spread function in the radar imaging field) vary with the positions. In this paper, we proposed an SV-CNN with spatial-variant convolution kernels (SV-CK). Its function is illustrated through a special application of enhancing the radar images. After being trained using radar images with position-codings as the samples, the SV-CNN can enhance the radar images. Because the SV-CNN reads information of the local position contained in the position-coding, it performs better than the conventional CNN. The advance of the proposed SV-CNN is tested using both simulated and real radar images.

Nonlinear iterative inversion methods are computationally expensive, which leads to limited applications. In this paper, a fast algorithm of the cross-correlated contrast source inversion (CC-CSI) method is proposed. By assuming a homogeneous background medium, the task of solving systems of linear equations, the most time-consuming part of the CC-CSI method, has been efficiently implemented with several FFTs and IFFTs for transverse magnetic (TM), transverse electric (TE), and 3-D inversion, respectively. Theoretical analysis and real experiments demonstrate that the inversion efficiency of CC-CSI has been improved dramatically in comparison to the strategies of LU decomposition and the Biconjugate gradient algorithm. Specifically, the inversion speed of the proposed fast CC-CSI algorithm is at least one order of magnitude higher than using the latter two approaches in 3-D inversion, while the memory requirement of the proposed algorithm is intermediary and acceptable. Furthermore, the proposed fast scheme is also applicable to all the inversion methods which are related to computing of the electric fields directly from the contrast sources in homogeneous background media.

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 ℓ ₁ -norm method are given to further demonstrate the efficiency of the proposed methods.