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.

A novel semantic Minimum Bayes ternary hypothesis detector based on the Rayleigh distribution is presented to decrease detection false alarm rate of synthetic aperture radar image. The method not only employs the strong scattering features of the target which is used in constant false alarm rate (CFAR) but employs the shadow features of the target which is used in the Power Ratio detector. Furthermore, target, shadow, and clutter regions are merged into the ternary image to estimate Rayleigh distribution parameters and weights. Meanwhile, the semantic relationship between the strong scattering features and the shadow features is established to partly reduce the false alarm targets. By the experiments on the Mini-SAR image of the 4-in resolution, it is shown that our method outperforms the semantic CFAR method and CFAR algorithm by a much lower false alarm rate.