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In recent years, Synthetic Aperture Radar (SAR) Tomography (TomoSAR) has ascertained great potential for the three-dimensional (3-D) reconstruction of observed scenes, especially in urban areas. However, the number of proceed snapshots (observations) is usually less than that of slant height samples (unknowns) in TomoSAR inversion processes. This impairs the quality of the reconstructed vertical information. To cope with this issue and improve the reliability of reconstructed vertical information, this paper investigates the possible potential of a deterministic descriptive regularization-based method. Deterministic descriptive regularization is a well-conditioned optimization framework based on the descriptive idea of a regularization solution. This strategy can help to mitigate the effect of the ill-posed problem. Thus, it can assist SAR tomography to deal with the possible impairing issues arising from low numbers and the distribution of baselines. For this purpose, the result of the proposed strategy is compared with the outcomes from the standard TomoSAR techniques, including Beamforming, Capon, and Minimum Norm. The proposed method for reconstruction of the reflectivity function of the observed scene has been performed on a dataset acquired by the Sentinel-1 sensor in 2022 over Tehran City, Iran. The experimental results indicate that the proposed algorithm can estimate building heights with a vertical accuracy of better than 91%. These results demonstrate the great potential of the proposed method for reconstructing the full 3-D images of urban areas. [ABSTRACT FROM AUTHOR]

In recent years, there has been a growing interest in the development of ground-based Synthetic Aperture Radars (GBSAR) for the purpose of monitoring structural displacements. GBSAR offers high-resolution monitoring over a wide area and can capture data every few minutes. However, compact high-frequency multiple input multiple output (MIMO) radars have emerged as an alternative for monitoring sub-second displacements, such as structural vibrations. MIMO radar has sub-second acquisition interval. However, it has limited cross-range resolution compared to GBSAR, and interference between antennas and presence of multiple scatterers in the scene can cause strong sidelobes in the processed data. On the other hand, GBSAR utilizes a long synthetic aperture to achieve high cross-range resolution. However, due to its longer data acquisition time compared to MIMO radar, conventional methods are insufficient for detecting scatterers' sub-second displacements that occur during the data acquisition process. This study proposes a method to effectively monitor sub-second or sub-minute displacements using GBSAR signals. The proposed method enhances the conventional radar interferometric processes by employing spectral estimation, allowing for multi-dimensional detection of targets' azimuth angle, linear displacement, and vibrational characteristics. Consequently, this method improves both the processing of MIMO radar data and enables high-resolution fast displacement monitoring from GBSAR signals. The paper presents the theoretical details and mathematical formulations of the proposed method for both MIMO radar and GBSAR imaging modes. To evaluate the effectiveness of the proposed method, numerical simulations and real experiments are conducted. The experimental results validate the capability of the proposed method in both GBSAR and MIMO configuration modes for high-resolution monitoring of fast linear displacements and vibrations. The results exhibit promising signal-to-noise ratio (SNR) and peak-to-sidelobe ratio (PSLR) values. [ABSTRACT FROM AUTHOR]