Space-ground bistatic configurations offer significant potential for anti-stealth and global coverage, overcoming the detection limitations of ground-based bistatic inverse synthetic aperture radar (Bi-ISAR) systems. However, achieving high-resolution Bi-ISAR imaging in this configuration remains challenging due to the complex observation model, particularly involving long dwell times and sparse aperture (SA) scenarios. This article proposes a high-precision imaging and cross-range scaling (CRS) scheme for space-ground Bi-ISAR under short-aperture observations, which employs second-order phase error approximation and formulates Bi-ISAR autofocusing and CRS as sparse time-frequency reconstruction problems within the Centroid Frequency-Chirp Rate (CFCR) domain. Furthermore, an adaptive iterative Wiener filter (AIWF)-based reconstruction algorithm is developed, which employs complex Gaussian and Generalized Double Pareto distributions for prior modeling of the original noise and the noise auto-term, respectively, facilitating Bayesian inference. By exploiting the correlation between cross-terms and signal components, the proposed method adaptively suppresses cross-terms, ensuring high-precision, cross-term-free sparse time-frequency reconstruction. Experimental results demonstrate that the proposed algorithm exhibits strong robustness in low signal-to-noise ratio (SNR) and high missing rate (MR) scenarios, achieving well-focused and high-resolution Bi-ISAR imaging even at an SNR of 0 dB or an MR of 70%.

Computational microwave imaging with metasurface aperture (MA-CMI) is an emerging real aperture imaging scheme. It is widely concerned because of its advantages of low hardware complexity, low manufacturing cost, and high sampling rate. However, the existing studies require the MA-CMI system to remain relatively stationary with the Region of Interest (ROI), which greatly limits its application. Again, if there is a relative motion between the MA-CMI system and the ROI, the correlation between the measured signal and the sensing matrix of the MA-CMI system will be lost, resulting in the defocus of the imaging results and the degradation of the imaging quality. In this paper, our work focuses on the problem that the imaging results are out of focus due to the unknown lateral motion between the MA-CMI system and the ROI, that is, the blind focus imaging of moving scenes based on the MA-CMI system. Firstly, according to the measurement mechanism of the MA-CMI system, an observation model that considers the lateral motion of the ROI is established. Subsequently, based on the model, we develop a robust alternate iterative method called Newton-Sparse Bayesian learning (Nt-SBL). Specifically, in each iteration, the Newton method was used to estimate the unknown velocity parameters of the motion scene; on the other hand, based on the current velocity estimation, the scene reconstruction was performed using the generic SBL. Finally, based on the MA-CMI system prototype we designed, both simulation and measured experiments are performed to verify the effectiveness of the proposed method.

In this article, the efficient sparse Bayesian learning (SBL)-based 2-D joint high-resolution inverse synthetic aperture radar (ISAR) imaging approach with random missing observations in both the range-frequency and slow-time domains caused by frequency agility and pulse repetition interval (PRI) jitter is proposed. First, the target return signal model containing the translational motion caused envelope migration and phase error and rotation caused range spatial-variant phase error (RSVPE) with 2-D randomly missing observations is established. Next, considering the rotation caused RSVPE needs to be estimated and compensated for each range cell individually in the range domain, the modified conditional mean estimator-based missing observations recover method and its fast implementation method based on fast Fourier transform (FFT) is designed. Following, the SBL-based cyclic iteration approach is proposed to recover missing observations, estimate target motion parameters and compensate for the translational motion and RSVPE, and achieve the focused and cross-range scaled ISAR image. In addition, to alleviate the computational complexity increase caused by data filling for SBL, a novel low cyclic displacement rank decomposition (LCDRD) for the Toeplitz-block-Toeplitz (TBT) structured covariance matrix of the completed observations in SBL is proposed and applied to design efficient SBL-based ISAR imaging algorithms for two different types of observations. Finally, the effectiveness of the proposed algorithms is validated using both simulated and measured data.

In this article, the problem of inverse synthetic aperture radar (ISAR) high-resolution imaging and cross-range scaling with periodically gapped coherent processing interval (CPI) caused by the radar performing multiple tasks time divisionally is addressed. In the case of periodically gapped CPI, the traditional fast Fourier transform (FFT) based ISAR imaging method is no longer applicable, and sparse reconstruction is an effective approach to solve this problem. Sparse Bayesian learning (SBL) is the most robust and accurate reconstruction method among all sparse reconstruction algorithms, and it is also an implementation of optimal estimation of the random signal model under the minimum mean square error (MMSE) criterion. Based on the fact that the noise variance of radar observation can be estimated with secondary data, and the amplitudes of the target scatterers can be regarded as unknown deterministic variables, we propose another implementation method for the MMSE estimator, i.e., iterative Wiener filter (IWF), for ISAR imaging and cross-range scaling of periodically gapped data. Compared with SBL, the proposed method has the advantages of lower computational complexity, faster convergence, and higher reconstruction accuracy. Further, we design two fast IWF algorithms based on the triangular-circulant low displacement rank decomposition by utilizing the Toeplitz-block-Toeplitz (TBT) structure, in which almost all operations except matrix decomposition can be calculated using FFT, which can efficiently and accurately process two different types of periodically gapped echo data. Finally, the performance of the algorithm was verified with both simulation and measured data.

For multifunctional phased array radar systems, inverse synthetic aperture radar (ISAR) imaging typically requires multidwell coherent processing to achieve adequate cross-range resolution. In such cases, the traditional fast Fourier transform (FFT)-based Doppler processing method can result in grating lobes in the cross-range dimension. Additionally, the range resolution is insufficient when the radar transmission bandwidth is relatively narrow. To address these two issues, this article proposes a fast sparse Bayesian learning (SBL)/iterative Wiener filter (IWF)-based 2-D joint super-resolution ISAR imaging method, which enhances the resolution in both range and cross-range dimensions while suppressing grating lobes. The proposed fast SBL and IWF algorithms incorporate the lower-triangular-Toeplitz-cyclic (LC) decomposition of the unfolded fourth-order Toeplitz tensor of the covariance matrix. Except for the LC decomposition, all operations utilize the FFT, allowing for efficient, precise, and memory-efficient processing of two types of multidwell observations. Furthermore, during image reconstruction, the target’s rotational velocity is estimated using the minimum entropy criterion, thereby achieving range-variant autofocus and 2-D super-resolution ISAR imaging. Finally, simulated and measured data are employed to validate the effectiveness of the proposed algorithms.

Micro-Doppler analysis of rigid-body target is significant for attitude estimation and recognition of space objects. The traditional micro-Doppler analysis method for rigid-body targets includes two sequential steps. First, the time-frequency analysis is performed on the radar echo data of the target, and then the micro-Doppler curve of each scattering center is separated and extracted from the time-frequency map. The second step depends on the micro motion model of the target. In the micro-Doppler analysis of real rigid-body target, there are some problems such as the mismatch of the micro motion model, the incidence angle dependence of the scattering center position, and the partial occlusion of the scattering center. Therefore, it is very difficult to correctly extract the micro-Doppler curves of multiple scatterers. In this paper, an end-to-end micro-Doppler analysis method for rigid-body target based on deep learning network is proposed, which can directly separate and extract the micro-Doppler curves of multiple scatterers from the target echo data. Specifically, an Asymmetrical AutoEncoding (A2E) network equipped with a Data Pre-Processing (DP2) module is developed to extract Time-Frequency Curves (TFCs) from radar echos. Considering the sparseness of Time-Frequency Distribution (TFDs), we then develop a novel Energy-Concentration Objective (ECO) function based on Min-Max game to enhance curves energy while suppress the background energy. In practice, measured TFDs are rarely annotated, it restricts the generalization capability of the A2E from the simulation to the measurement. To bridge the gap, two-fold modifications are finally constructed: i) we insert a partial-shared branch of decoder to reconstruct the TFD from the DP2 module; ii) we regularize the ECO function with a knowledge preservation based reconstruction bound to further capture the characteristics of measured echos in a semi-supervised way at test time to relieve the domain-shift problem.

Sparse aperture (SA) autofocusing and imaging is a hot research problem in the signal processing field and has been widely used. Under SA, the absence of echoes destroys the coherence between the pulses, which then affects the autofocusing accuracy of the imaging, leading to defocus of the image. In this article, a novel SA autofocusing and imaging algorithm based on sparse Bayesian learning (SBL) is proposed, which uses a fast SBL algorithm to achieve SA high-resolution imaging and the minimum Tsallis entropy algorithm to realize autofocusing. As is known to all, SBL has strong robustness and high precision. Unfortunately, the direct calculation of the inversion and multiplication operations involved in each iteration of SBL results in significant computational costs. In the proposed fast SBL algorithm, the matrix required to be inverted has a special structure. The inverse matrix can then be represented by Gohberg–Semencul (G–S) factorization. Also, almost all operations except for G–S factorization during each iteration can be completed by fast Fourier transform (FFT) or inverse FFT (IFFT), which greatly reduces the amount of computation by several orders of magnitude. In each SBL iteration, the minimum Tsallis entropy algorithm is used for estimating the phase error, which has better noise sensitivity and obtains the images with the best focused degree. Finally, the effectiveness and high efficiency of the proposed fast algorithm are verified by experimental results obtained by simulation and measured data.

Computational microwave imaging (CMI) based on the frequency diversity metasurface apertures (FDMAs) is an emerging technology and has attracted wide attention. FDMA based CMI (FDMA-CMI) can be considered as microwave compressive sensing imaging with the frequency diversity pattern of the FDMA being the sensing matrix and solved by sparse signal reconstruction algorithms. However, the imaging quality is affected by the sensing matrix error and off-grid error seriously. In this paper, we propose a novel algorithm for FDMA-CMI, referred to as OGSISBL, by taking both the off-grid error and sensing matrix error into account. Firstly, we establish the measurement model with both the off-grid error and sensing matrix error. Specifically, the off-grid error is represented as a set of parameters to be estimated in the measurement model and the sensing matrix error is represented as the amplitude-phase drift of the transceiver channels of the imaging system due to the principle of the FDMA. Then, under the framework of the sparse Bayesian learning, a robust imaging algorithm OGSISBL is developed via the variational Bayesian expectation maximization (VBEM), which can not only recover the amplitude and position of the return of the scattered, but also simultaneously calibrate the amplitude-phase drift of the transceiver channels and the off-grid error. The performance of the proposed algorithm is evaluated by both the simulation data and the measured data collected by the self-designed experimental FDMA-CMI system, and the results validate the effectiveness and robustness of the proposed method.

Sparse Bayesian learning (SBL) is a popular and robust algorithm for sparse signal reconstruction (SSR). Unfortunately, the SBL algorithm suffers from heavy computational complexity when it is implemented directly since the inversion and multiplying operations of the estimation of the covariance matrix are involved in each iteration, which is proportional to the cube of the observed data length and thus prevents it solving large-scale problems. In many applications, such as radar imaging and array signal processing, the signal to be recovered is sparse in the Fourier dictionary. In this article, we propose an efficient implementation method for the Fourier dictionary-based SBL (FD-SBL). In the case that the Fourier dictionary is adopted, the estimation of the covariance matrix is a Toeplitz matrix for 1-D data or a Toeplitz-block-Toeplitz (TBT) matrix for 2-D data during the FD-SBL iterations. By utilizing this property, we employ the Gohberg–Semencul (G-S)-type factorization to accelerate the implementation of FD-SBL. To be noted, there is no approximation in our proposed method, and the computational cost is reduced by several orders of magnitude compared with the direct implementation of SBL. Finally, the experimental results verify the effectiveness of the proposed method.

Computational microwave imaging with frequency-diverse metasurface (FDM) apertures is an emerging technology. In this article, we establish an experimental FDM microwave imaging system and address the waveform design problem based on the information theory, aiming to enhance the advantages of the FDM imaging. Two waveform design methods based on the different criteria are proposed for the FDM imaging system. The first waveform is designed by maximizing the mutual information between the object and the measured data with the constant transmitted energy, and the second one is designed by minimizing the transmitted energy while the mutual information is not less than a threshold. The performance of the proposed waveform design methods is evaluated by the data gathered by the self-established experimental FDM imaging system. The results show that the proposed waveform design methods are capable of improving the imaging quality or the imaging efficiency of the FDM imaging system.

Micro-Doppler radar signatures are capable of characterizing rich motion information of targets and have played important roles in target identification and recognition. In this letter, we develop a novel parametric time-frequency method to analyze the micro-Doppler signatures of rigid-body targets, which is referred to as the block-sparse forward-backward time-varying autoregressive (BS-FBTVAR) model. First, the basis expansion method is employed to convert the time-varying model parameter estimation problem to be time invariant. Then, by investigating the intrinsic relationship between the model parameters and the poles of rigid-body targets, block-sparsity constraints are introduced to the conventional FBTVAR model. A complex-valued block-sparse Bayesian learning algorithm is developed as the solver of the novel BS-FBTVAR model. Finally, experiments on the electromagnetic (EM) analysis data are carried out to validate the performance of the proposed method.