• In response to the azimuth defocusing issues caused by target motion, a sparse recovery model capable of characterizing target phase errors is established, and an autofocusing module based on the maximum contrast criterion is proposed, achieving the estimation of azimuth phase errors. • Considering the low-rank characteristics of the THz-SAR moving target range profile matrix, the dispersed nature of the background range profile, and the sparsity of the moving target image, the concept of Robust Principal Component Analysis (RPCA) is introduced. By integrating the aforementioned autofocusing module, a THz-SAR moving target imaging algorithm based on low-rank and sparsity joint constraints, AF-RPCA-ADMM, is proposed, achieving the separation of moving targets from the background and focused imaging. • To accelerate the imaging algorithm, an efficient HR imaging network for moving targets, AF-RPCA-Net, based on a deep unfolding network, is designed. The network automatically learns the optimal hyperparameters required for each iteration process of the sparse recovery algorithm, resulting in well-focused THz-SAR moving target images efficiently. Terahertz-Synthetic Aperture Radar (THz-SAR) offers high frame rates and high resolution, making it particularly suitable for remote sensing applications, like dynamic monitoring of moving targets. However, due to the non-ideal motion of the airborne platform and the non-cooperative motion of targets, this phenomenon causes more severe defocusing compared with microwave band SAR. Traditional SAR imaging methods, if directly applied to image THz-SAR moving targets, often suffer from poor quality and low efficiency. To address this issue, this article proposes a moving target non-parametric learning imaging method based on the Deep Unfolding Network (DUN) framework. Firstly, an autofocusing module is derived based on the maximum imaging contrast and embedded within the Alternating Direction Method of Multipliers (ADMM) iterative solution process to achieve accurate compensation of azimuthal motion errors. Then, we introduce the concept of Robust Principal Component Analysis (RPCA) to achieve sparse recovery imaging of moving targets. Finally, based on the ADMM iterative solution process, we establish an imaging network, named AF-RPCA-Net, efficiently achieving model-data jointly driven moving target background separation and imaging. The proposed method is validated to be effective and efficient through experimental results derived from both simulated and measured data.

Sequential ground moving target imaging (GMTIm) is an imperative and challenging task under terahertz video synthetic aperture radar (THz-ViSAR), which contributes to fine-grained situational awareness and moving target (MT) recognition. However, traditional GMTIm methods are usually designed for single-frame images, which involves repetitive parameter estimation for the sequential imaging problem and lacks the efficiency due to the parameter sensitivity. To tackle the aforementioned problems, this paper proposes a sequential GMTIm method based on hybrid THz-ViSAR-inverse SAR (ISAR) image formation. With respect to ViSAR processing, the sequential imaging results are firstly obtained. Considering the similarity of scene among inter-frame images, MTs can be detected based on target-level change detection after image registration and shadows left on the road. Following this, the defocused target region is transformed to obtain raw echoes, which is beneficial for parallel processing and reduce the computation amount. As for ISAR processing, the envelope alignment and auto-focus methods are employed to eliminate the residual motion errors and compensate for phase errors without constructing prior motion patterns. Thereafter, the ratio of equivalent rotational velocities between MTs and the scene is estimated to achieve the azimuth scaling. Finally, sparsity-based imaging enhancement is employed to further enhance the imaging quality. Simulations and airborne experiments are carried out to validate the effectiveness of the proposed method.

Ground moving target imaging (GMTIm) presents both challenges and opportunities for enhancing the fine-grained situational awareness and target recognition. However, the imaging quality of non-cooperative moving targets (MTs) fundamentally depends on their motion characteristics, which often fluctuate unpredictably during long dwell times in microwave bands. To address these limitations, this paper proposes a robust GMTIm scheme based on terahertz video synthetic aperture radar (THz-ViSAR). Rather than operating on complete echo data directly, the proposed method achieves GMTIm through the defocused region of interest (RoI) data inversion, which can reduce the computation burden. Benefiting from the short dwell time of THz-ViSAR, motion patterns of MTs can be simplified as the uniform motion in most cases. In response to range walk (RW) manifested by radial motion of MTs, the RW correction is employed based on the inclination of range profiles. Thus, considering the sparsity of MTs, motion errors caused by azimuth velocities from MTs, can be compensated by the minimum image entropy-based alternating direction method of multipliers (ADMM) autofocus framework, which can deal with the unknown phase errors and improve the imaging quality adaptively. Finally, the azimuth scaling is established by the azimuth spreading coefficient table, which is constructed based on the target velocity, rotating radius and center angle. Simulations and airborne field experiments are carried out to validate the effectiveness of the proposed method.

Array-based millimeter wave (MMW) holographic imaging technology has shown great application potential in nondestructive evaluation (NDE) of dielectric materials (such as composites). With the development of high-precision motion capture systems, the NDE of the internal structure of layered dielectric targets by handheld radar has become a new demand growth point. Since the elements of the handheld-radar-based array are randomly distributed in the 3-D space, the existing fast-imaging algorithms are difficult to be directly applied, which will restrict the development of this application. For this reason, this article proposes a fast-imaging algorithm for layered dielectric targets based on spatial 3-D nonuniform single-input single-output (SISO) array radar. The algorithm takes each element of the spatial 3-D random array as the center, expands it into a virtual uniform plane array, then transforms the echo data of the virtual array from the spatial domain to the wavenumber domain by using fast Fourier transform (FFT). After phase compensation, the wavenumber-domain data of all virtual arrays are added, to obtain the wavenumber-domain scattered echo data of the entire 3-D nonuniform SISO array radar. Finally, the imaging result of the target is obtained through the 2-D inverse Fourier transform (IFT) in azimuth direction and the segmented IFT in range direction. Numerical simulation and experimental measurements show that the proposed algorithm can significantly improve the imaging efficiency compared with the improved back-projection (IBP) algorithm which is also suitable for this scenario.

Airborne terahertz video synthetic aperture radar (THz-ViSAR) exhibits excellent superiorities in the dynamic situation awareness and moving targets detection. However, limited by the recording precision of the inertial navigation system (INS) or global positioning system (GPS), data-driven motion compensation (MOCO) methods are challenging to eliminate motion errors for THz band. Particularly, platform vibrations that are previously negligible in the microwave band, become non-negligible, drastically degrading the focusing performance. To conquer aforementioned problems, this paper proposes an echo-driven robust MOCO framework suited for THz-ViSAR. First, the airborne motion error model (MED) is re-derived and corresponding effects are analyzed in detail. Based on the derived MED, two parts are required to estimate from the echo: radial errors and vibration errors. Thus, a forward estimation of candidate signal of interests (SoIs) is proposed based on local peaks of the average range profile and the prominence. For each candidate, radial and vibration errors are estimated from the unwrapped phase of the SoI via the polynomial and multi-component sinusoidal fitting in turn. Finally, MOCO functions are constructed and evaluated based on the image entropy and image contrast, which determines the optimal SoI. Airborne field experiments are carried out to validate the effectiveness and practicability of the proposed method.

Rotating targets/components often carry beneficial information for identifying high-value targets in video synthetic aperture radar (ViSAR). However, unlike linear motion models, rotating motion models involve more parameters to be estimated, rendering parametric-based methods computationally intensive. Besides, such micro-motion features are relatively insignificant in the microwave band. To conquer the aforementioned problems, this article proposes the nonparametric indication and imaging of rotating targets under terahertz (THz) ViSAR. Taking rotating corner reflectors (RCRs) as the object, the Doppler prior and imaging characteristics (DPIC) are first determined and regarded as the theoretical basis. Combining DPIC and Doppler sensitivity of THz band, RCRs can be easily indicated by the nonparametric time–frequency transform. Thus, range cells of RCRs can be deduced intuitively by the visual saliency, followed by the separation of the residual background and defocused target area. After clutter suppression, two signal of interests (SoIs) of RCRs are extracted from salient points, where unwrapped phases and azimuth spectrums are utilized for fast estimation of phase errors and additional Doppler centroids (DCs), respectively. Finally, the refocused target image is stitched into the residual background. To validate the effectiveness of the proposed method, the airborne field experiment of RCRs is conducted in THz-band for the first time. Moreover, the anti-noise ability, relocation capability, and applicable speed interval of the proposed method are demonstrated, along with its extended application potential in terms of the ground moving target imaging.

The high-resolution inverse synthetic aperture radar (ISAR) imaging of space target holds tremendous significance for recognition and on-orbit maintenance. The terahertz (THz) radar possesses natural superiority in terms of large bandwidth and short wavelength, enabling it to achieve higher resolution both in range and azimuth directions. However, the range cell migration (RCM) induced by rotation is severe in the THz band, even in small rotation angle. In order to achieve high-accuracy RCM correction, an imaging algorithm based on keystone transform (KT) and fast Gaussian gridding nonuniform fast Fourier transform (FGG NUFFT) is presented in this article. Nevertheless, to correct the second-order RCM and compensate the spatial-variant (SV) phase error, the rotation parameters of uncooperative target need to be estimated first. Moreover, by analyzing the ISAR images of space targets, it is found that the scattering intensity of certain components on the satellite body, such as the cavity structure of the antenna, is stronger than that of the solar panels. Considering scattering intensity of these components, the traditional estimation method under global image quality criteria may fail. To prevent getting trapped in a local optimum or finding an incorrect solution due to the influence of strong scattering points, a parameter estimation framework based on prior knowledge added sparrow search algorithm (PKSSA) under local maximum contrast criterion (LMCC) is brought forward. The proposed novel algorithm can not only fast estimate rotation parameters without being affected by strong scattering points but also obtain fine imaging results. Numerous electromagnetic simulation and real measured THz experiment results prove the correctness and effectiveness of the proposed algorithm.

As demand for precise detection of space targets and orbital maintenance increases, it is crucial to obtain high-resolution images of space targets. The terahertz (THz) radar with carrier frequency of 0.1-10 THz has the characteristics of larger bandwidth and shorter wavelength compared with microwave radar. Accordingly, under the same inverse synthetic aperture radar (ISAR) imaging conditions, it has advantages in both range resolution and azimuth resolution theoretically. However, for large-size space targets, the phenomenon of high-order range cell migration (RCM) and azimuth phase error are prone to occur during small-rotation-angle (3-5°) ISAR imaging, which results in severe imagery defocusing. In this article, a high-resolution ISAR imaging method based on defocused point spread function (PSF) is proposed. By means of third-order Taylor expansion performing on the Range-Doppler (RD) imaging model, the impact of high-order terms on imaging is analyzed. Through revealing the relationship between high-order terms and inclination of defocused PSF measured with Hough Transform (HT), the rotation velocity and range center deviation (RCD) are estimated accurately and independently in image domain. After parameters estimation, the first-order RCM is corrected by Keystone Transform (KT). Utilizing the estimated rotation velocity, the second-order RCM is eliminated by Fast Gaussian Gridding Nonuniform Fast Fourier Transform (FGG NUFFT). Then the spatial-variant phase error is compensated based on previous estimation. Lastly, azimuth resolution is improved by FGG NUFFT due to non-uniformly sampled data. Numerous simulations and real measured experimental results demonstrate the effectiveness and outperformance of proposed algorithm for large-size space target ISAR imaging in the THz band.

Terahertz (THz) inverse synthetic aperture radar (ISAR) imaging of space targets has the advantage of high resolution and all-day capability for spatial situational awareness (SSA). However, compared with microwave ISAR imaging, microvibrations of the radar platform and target can cause image defocusing and quality degradation in the THz band. Commonly, the existing algorithms considered vibration as simple harmonic motion in a rigid body and estimated the vibration parameters for phase error compensation. Nevertheless, these methods are dependent on the prominent points and cannot focus on the complex nonrigid vibration of the space target. Aiming at these problems, an ISAR imaging framework that can be leveraged for complex nonrigid vibration compensation is proposed. First, a compressed sensing (CS) model is established to compensate for the vibration phase error in ISAR imaging. Then, the alternating direction method of multipliers (ADMMs) is employed to optimize the CS model. Subsequently, considering that strong scattering points of space targets will cover up the weak scattering information in ISAR images, a sidelobe suppression constraint is appended. Thus, the weak scattering information is retained while removing the sidelobe and noise. It is worth mentioning that the ISAR imaging algorithm is derived to a 2-D matrix form to reduce memory usage and improve computational efficiency. Finally, simulated and measured data are utilized to verify the superiority of the proposed algorithm and prove the potential of ISAR imaging for practical space targets.

Video synthetic aperture radar (ViSAR) operating at low-frequencies generally suffers from low frame-rate and high latency due to its wide synthetic aperture and long dwell time. To conquer the problems mentioned above, this article proposes a ViSAR imaging processing framework based on the terahertz (THz) regime. The proposed method only needs a data repetition ratio of 0% rather than 80% for the microwave to reach the 0.2m imaging resolution and 5Hz frame rate with low latency thanks to the designed high pulse repetition frequency (PRF) system and short wavelength of THz wave. Thus, robust estimations of baseband Doppler centroid and Doppler rate are proposed based on the multi-core adaptive weighting and imaging knowledge prior, which handles the Doppler sensitivity of the THz regime effectively. Finally, airborne experiments are carried out to validate the superiority of dynamic situational awareness and the potential of moving targets indication in the THz-ViSAR.

Terahertz coded aperture imaging (TCAI) is a promising radar imaging technology that leverages coded aperture antenna to achieve forward-looking imaging without relying on relative motion. For solving the target scattering coefficient, one typical approach is to impose generic sparsity prior constraint in the image domain. Although the method has made significant progress in TCAI, it is still challenging to achieve the high-resolution reconstruction of targets with different sparseness under compression measurements, and it is also limited by poor noise resistance performance. To tackle these problems, we propose a new imaging scheme using deep prior captured by the generator. In this letter, we first analyze and model the system based on a coherent detection array and propose a deep prior-based model for TCAI by modeling the target as being in the range of the generator. Then, the deep alternate minimization (Deep-AM) algorithm is designed to solve the model by projecting between the target space and the latent variable space in an alternating fashion. Finally, the simulation results demonstrate the robustness and effectiveness of the proposed approach under the compression measurements. Also, the acquisition and coding times of the system are greatly reduced by utilizing array receiving and deep prior information.

Terahertz (THz) regime has shown superior performance in terms of reflecting the details of target structures. However, the extended structures (ESs) may be discretized into endpoints in synthetic aperture radar (SAR) images if the observation aperture deviates from the specular orientation of ESs, which deteriorates subsequent image interpretation and intelligent imaging. Taking the tank barrels as the object, this paper proposes a novel solution to detect and reconstruct the critical ES by effectively exploiting the component prior and imaging characteristics (CPIC). The core of the proposed method lies in converting the phase matching of the multi-views methods into object detection based on CPIC and deep neural network. Firstly, the CPIC of tank barrels is analytically determined and regarded as the theoretical basis of datasets annotation. Thus, the modified multi-scale object detection network is constructed to enhance the detection performance and estimate the orientation of barrels. Finally, comprehensive simulation, anechoic chamber and field experiments are carried out to validate the effectiveness of the proposed methods. The results show that the proposed method can outperform the existing object detection networks in terms of the detection accuracy of multi-scale objects, and outperform the existing multi-view methods in terms of time need with comparable accuracy.

Raw signal simulation is an important tool to test the effectiveness of the system parameters and imaging algorithms. A fast raw signal simulation method for multi-circular synthetic aperture imaging is proposed based on the inverse processing of the imaging algorithm and the nonuniform fast Fourier transform. The analytical description and processing procedure are presented. Simulation results of an ideal point target and a human model demonstrate the validity and effectiveness. Compared with the common time-domain method, the proposed method can achieve equivalent performance with higher efficiency.

Convolutional neural networks (CNN) have successfully been employed to tackle several remote sensing tasks such as image classification and show better performance than previous techniques. For the radar imaging community, a natural question is: Can CNN be introduced to radar imaging and enhance its performance? This letter gives an affirmative answer to this question. We first propose a processing framework by which a complex-valued CNN (CV-CNN) is used to enhance radar imaging. Then we introduce two modifications to the CV-CNN to adapt it to radar imaging tasks. Subsequently, the method to generate training data is shown and some implementation details are presented. Finally, simulations and experiments are carried out, and both results show the superiority of the proposed method on imaging quality and computational efficiency.

Recently, millimeter-wave (MMW) 3D holography techniques employing a scanning 1D multiple input multiple output (MIMO) array have shown several superiorities for short-range applications than traditional single input single output (SISO) ones. However, current imaging algorithms for this emerging regime are not satisfied, either too slow as a back projection (BP) manner is used or of poor quality since several steps of approximations are introduced. In this paper, two fast fully-focused imaging algorithms are developed towards fixing these drawbacks. Both algorithms are based on the assumption that the receivers are evenly distributed. The first algorithm further hypothesizes that the transmitters are also evenly located, while the second algorithm needs looser restrictions that the transmitters can be arbitrarily positioned. The frequency domain expressions of the modified Kirchhoff method are also derived and used to promote the precision of the proposed algorithms. In addition, several implementation issues including resolution, sampling criteria and computational complexity are discussed. Finally, both simulation and experimental results validate the effectiveness of the proposed methods on reconstruction quality and computational efficiency.

A novel 3-D surface imaging method based on terahertz (THz) dual-frequency interferometry is proposed for the detection and imaging of metal objects. The interferometer is formed first in the range direction with two azimuth–elevation images at different THz frequencies. Then, the 3-D surface image can be obtained by interference processing of two azimuth–elevation imaging results. Compared with the traditional wideband 3-D imaging, the proposed method can avoid the nonlinear error caused by the signal nonlinearity. In addition, the image registration for the interference processing is evitable, when the frequency difference satisfies certain conditions. Based on the electromagnetic calculation data, the 3-D surface imaging results of both rough cone and rough cube validate the effectiveness of the proposed method. Furthermore, the reconstruction error increases slightly with the increasing of the error of frequency difference, which indicates that the proposed method has a good tolerance with respect to frequency instability.

This paper presents a detection algorithm for micromotion targets, such as rotating antennas, in the synthetic aperture radar (SAR) geometry. It utilizes target's range cell migration characteristics, i.e. a micromotion target takes on a sine cure in the slowtime-range image, but with incontinuity or gaps when clutter (and part of target energy) is suppressed. Two-stage detection, including MTI and the extended Hough transform, is used to suppress clutter and to extract the sine curve. Quasi-real SAR data of Isleta Lake demonstrate high SNR gains and good detection performance.

Compressed sensing theory has been successfully applied to the target parameter estimation in ultra-wide-band (UWB) radar system. Compared to Nyquist sampling method, far less samples are needed to recover the parameter of the target echo. However, the existence of narrowband interference (NBI) changes the structure of the received signal seriously. NBI suppression problem must be considered to ensure the accurate parameter estimation of the targets. In this paper, we devote to the precise reconstruction of the received signal and propose a two stage OMP algorithm that can achieve target parameter estimation one time faster than the general multi-component dictionary method. Simulation results show the effectiveness of the proposed algorithm for NBI suppression and target parameter estimation.

A novel algorithm is proposed for detecting and estimating vibrating targets in synthetic aperture radar (SAR) data based on a pulse-repetition-interval (PRI) transform. Azimuthal signals of vibrating targets can be modelled as sinusoidal frequency-modulated (SFM) ones. The algorithm utilises the resemblance between the Doppler spectrum of vibrating-target SFM signals (or ghost image) and a pulse train, and applies to the spectrum the PRI transform originally used for estimating PRIs of pulse trains. The algorithm can detect SAR vibrating targets under moderate signal-to-noise/clutter ratios, and is also capable of accurately estimating the vibration frequencies even if there are multiple targets in a single range cell. The algorithm proposed has been successfully applied to both simulated and quasi-real data, and compared with that of the autocorrelation method, showing its superiority.

Fast raw-signal simulation is of considerable value for missile-borne synthetic aperture radar (SAR) algorithm development. On the basis of the two-dimensional (2-D) Fourier simulation method for stripmap SAR, we present a fast echo simulation method suitable for missile-borne SAR diving with constant acceleration. The analytical expression for the 2-D signal spectrum is derived and then converted to a stripmap one. Simulation results for a point target and a real scene demonstrate its validity and effectiveness.

This paper analyzes the influence of typical target micromotions on synthetic aperture radar (SAR) images, azimuth resolution limit, SAR/ground moving target indication (GMTI), and MTI. According to the micromotion periods contained in the coherent processing interval, a new range model expansion and a generalized paired echo principle are proposed and applied to underlie the analysis. Several new kinds of image characteristics including gray strips, ghost points, and fences are reported, which are sheerly distinct from those of slow movers. Micromotion will also cause a prominent range cell migration even if its amplitude is far smaller than the range resolution. SAR/GMTI and MTI techniques will, in general, become invalid for micromotion targets. The influence is eventually demonstrated by the simulated data in the airborne single-channel geometry, and it can be used for SAR image interpretation as well as passive jamming.

The range Doppler algorithm (RDA) is based on Taylor series expansion for the transfer function (TF) phase component, resulting in increasing phase error as the range frequency or the squint angle increases. We introduce Legendre orthogonal polynomials into synthetic aperture radar data processing steps to replace Taylor series expansion used in approximating the TF phase. A novel range Doppler imaging approach based on Legendre expansion is addressed with an extended RDA as example, and the analytical expressions of the new phase multiplication factors are then derived. The simulation results show that the proposed method provides better focusing performance than the conventional RDA in the same squint case and is more suitable for the large squint mode while there is negligible increment of computation load.