Synthetic Aperture Radar (SAR) imaging relies on using focusing algorithms to transform raw measurement data into radar images. These algorithms require knowledge of SAR system parameters, such as wavelength, center slant range, fast time sampling rate, pulse repetition interval, waveform, and platform speed. However, in non-cooperative scenarios or when metadata is corrupted, these parameters are unavailable, rendering traditional algorithms ineffective. To address this challenge, this article presents a novel parameter-free method for recovering SAR images from raw data without the requirement of any SAR system parameters. Firstly, we introduce an approximated matched filtering model that leverages the shift-invariance properties of SAR echoes, enabling image formation via convolving the raw data with an unknown reference echo. Secondly, we develop a Principal Component Maximization (PCM) method that exploits the low-dimensional structure of SAR signals to estimate the reference echo. The PCM method employs a three-stage procedure: 1) segment raw data into blocks; 2) normalize the energy of each block; and 3) maximize the principal component's energy across all blocks, enabling robust estimation of the reference echo under non-stationary clutter. Experimental results on various SAR datasets demonstrate that our method can effectively recover SAR images from raw data without any system parameters. To facilitate reproducibility, the Matlab program is available at https://github.com/huizhangyang/pcm.

Synthetic aperture radar (SAR) can produce well-focused images based on accurate observation models. However, motion errors in the data acquisition process often introduce inaccuracies in the models and degrade the image quality. Classical motion compensation (MOCO) methods can mitigate this problem, but they are not applicable to compressed sensing (CS) SAR imaging. Existing CS SAR imaging methods can jointly estimate and compensate the motion error from the data by iterative optimization, but they incur a high computational cost. To solve these problems, in this article, we propose an efficient data-driven MOCO strategy for CS SAR imaging. Specifically, we develop a two-step measurement estimation scheme followed by a fitting and filtering procedure to extract the motion error from the data. Then, we use the estimated motion error to correct the CS SAR observation model and reformulate a sparse SAR reconstruction problem based on the corrected model. This strategy significantly reduces the computational cost compared with existing CS SAR MOCO methods. To further expedite the image recovery, we design a fast imaging algorithm that exploits the feature of the observation matrix to accelerate the matrix-vector products and the interpolation operations involved in the recovery problem. Experimental results show that the proposed method can efficiently reconstruct SAR images from CS SAR data with motion errors and offer favorable imaging performance.

This article proposes a novel eigenvalue-based detector, called Lambda-1 detector, for adaptive and robust interference detection in single-look-complex (SLC) synthetic aperture radar (SAR) images. The proposed method leverages the increased eigenvalues caused by interference in SAR image blocks, where the interference is expected to have a small set of eigenvalues, particularly with a dominating one. Specifically, the method segments the image into multiple blocks, computes the eigenvalues of each block’s covariance matrix, and compares the largest eigenvalue$\lambda _{1}$with a threshold to determine the presence of interference under the criteria of constant false alarm rate (CFAR), thereby enabling adaptive interference detection against varying levels of interference-to-signal ratios (ISRs). The largest eigenvalue is characterized by the order-2 Tracy-Widom distribution (no closed-form expression) under the assumption of the image’s homogeneity, and the threshold is adaptively determined based on a scaled and shifted Gamma distribution that fits this distribution with a closed-form expression. The method is robust by first modeling and then correcting the impacts of upsampling and windowing of SAR image data on the fit distribution’s parameters, and by incorporating outlier removal preprocessing. Experimental results validate the effectiveness of the proposed method in successfully detecting both strong and weak interferences in various SAR images, including Sentinel-1 and Gaofen-3. The detection performance is quantitatively evaluated using false alarm rate$P_{\mathrm { fa}}$and detection rate$P_{d}$. In summary, the proposed Lambda-1 detector effectively identifies interference artifacts in focused SAR images and holds promise for improving the quality of SAR imagery by incorporating adaptive interference removal.

Compressed sensing (CS) synthetic aperture radar (SAR) can recover images from undersampled SAR data based on accurate observation models. However, motion errors often cause inaccuracies in observation data and result in defocusing of the reconstructed SAR images. Existing methods can restore and compensate the motion error from data by iterative optimization, which, however, leads to significantly increased computational cost. In this article, we propose an efficient motion compensation (MOCO) scheme for CS SAR using measured antenna phase center (APC) data. Specifically, we exploit the motion error measured by the navigation device to correct the CS SAR observation model. Then, we use the corrected model to formulate a new sparse SAR reconstruction problem. This leads to substantially lower computational cost than the existing MOCO methods in CS SAR. To further achieve fast image recovery, we design a fast imaging algorithm for CS SAR with MOCO to speed up some matrix–vector products involved in the reconstruction problem. The experimental results demonstrate that the proposed method can efficiently reconstruct SAR images from CS SAR data with motion errors.

Due to spectrum sharing spaceborne synthetic aperture radar (SAR) often experiences signal interference emitted by ground radio systems. Interference removal methods for SAR images are important measures to address this problem. Among these methods, block subspace filtering (BSF) has the advantage of removing various types of interference signals directly in single look complex (SLC) images. However, it assumes that the observation scene does not contain strong point scatterers, otherwise, BSF will have severe performance decline in terms of losing strong point scatterer intensity and causing horizontal or vertical black lines. This paper proposes a Robust version of BSF (RBSF), which can successfully overcome the above performance decline, thereby significantly improving the robustness of the algorithm. Specifically, RBSF uses a constant false alarm rate detector to detect and mask out strong scattering pixels from the SLC image. Then, BSF reconstructs the interference components from the SLC image with strong pixels being masked out, and finally subtracts them from the original SLC image. Moreover, we find that interference will reduce, to some extent, the image contrast and entropy. Based on this finding, we design an adaptive RBSF method which selects the subspace dimension parameter adaptively by means of optimizing the image contrast and entropy. Extensive experiments demonstrate that the RBSF algorithm achieves significant performance improvement over the original BSF algorithm.

Synthetic aperture radar (SAR) systems employ active imaging modes to collect observation data. However, restrictions such as power constraints often necessitate SAR systems to operate with a limited operational duty cycle, resulting in considerable idle time per orbit. This article introduces two innovative observation modes for SAR systems, aiming to effectively utilize this idle time for localizing terrestrial emitters, such as radar and communication systems, in the azimuth-range plane of SAR observation geometry. The proposed modes leverage passive observation capability of SAR systems and work in low power during time slots not dedicated to active imaging. The implementation first involves establishing observation geometries and positioning planes for SAR systems moving along linear and circular trajectories. Next, two passive observation modes are designed, utilizing two azimuth receive beams to gather observations from distinct angles along linear and circular trajectories, respectively. Subsequently, parametric models of beam center crossing times (BCCTs) are then developed, with the emitter coordinate as model parameters. Analytical and numerical positioning methods are proposed by inversing the model parameters. Additionally, Cramer–Rao lower bounds (CRBLs) are derived for the emitter coordinate under the proposed observation modes, and it is demonstrated that the proposed estimators achieve these theoretical bounds. Finally, several simulation experiments are conducted to analyze the performance of the proposed modes and methods.

Signals from ground-based emitters frequently cause interference to synthetic aperture radar (SAR). A typical class of such interference signals is the transmitted pulses of ground-based radar systems due to the spectrum sharing between the Earth exploration-satellite service (active) and radiolocation in International Telecommunication Union radio regulations. In this paper, we study the localization model and method of ground-based pulse emitters using SAR as the observation platform. Specifically, we first establish a nonlinear parametric observation model of pulse time of arrival (PTOA) based on SAR observation geometry, where the model parameters include the emitter position in SAR range-azimuth plane. Then, we approximate the PTOA observation model by a second-order polynomial, and estimate the azimuth and range positions of the emitter from the polynomial coefficients. Finally, we perform numerical experiments to test the accuracy of the proposed PTOA localization method. The results show that our method can achieve meter-level azimuth accuracy and kilometer-level range accuracy. Moreover, we study the Cramér-Rao lower bound (CRLB) of the emitter location, and by comparison, we show that the root mean square error of the proposed method is only about 1.5 times coarser than that of CRLB, demonstrating that our method achieves near-optimal localization accuracy.

Synthetic aperture radar (SAR) is an important imaging tool in many applications. Its imaging quality can be easily degraded by radio-frequency interferences (RFIs), among which the narrowband ones are typical. In recent years, it is shown that the narrowband RFI has a low-rank property and this property can be combined with the sparsity of radar echoes' to develop efficient RFI-suppression algorithms. However, these works usually consider the case of sparse echoes in the impulse-based radar, which is not suitable for typical SAR systems that use a chirp signal with a relatively long pulse duration. Some works adopt a large 2-D dictionary to introduce sparse representation for the echoes, which nevertheless lack efficient numerical algorithms, because the large dictionary brings high storage cost and computational burden. Motivated by these problems, this letter introduces an operator modeling approach for the echo dictionary and proposes a dictionary-based SAR RFI-suppression method under the framework of robust principle component analysis (RPCA). In the proposed method, the useful echo is sparsely represented by a dictionary, and the dictionary's analysis and synthesis operators are modeled as two sequences of low-cost operations by exploiting the chirp scaling algorithm. Then, an efficient algorithm is derived for solving the dictionary-based RPCA problem. Numerical simulations show that the proposed method is robust and efficient for SAR narrowband RFI suppression.

Radio frequency interference (RFI) can significantly pollute synthetic aperture radar (SAR) data and images, which is also harmful to SAR interferometry (InSAR) for retrieving elevational information. To address this issue, in recent years, a class of advanced RFI suppression methods has been proposed based on narrowband properties of RFI and sparsity assumptions of radar echoes or target reflectivity. However, for SAR echoes and the associated scene reflectivity, these assumptions are usually not feasible when the imaged scene is spatially extended. In view of these problems, this study proposes an InSAR-based RFI suppression method for the case of extended scenes. For this task, we combine the RFI-polluted SAR data with RFI-free interferometric data to form an interferometric SAR data pair. We show that such an InSAR data pair embeds an interferogram having the image amplitude multiplying by a complex exponential interferometric phase. We treat the interferogram as a kind of natural image and use discrete Fourier cosine transform (DCT) for its sparse representation. Then combining the DCT-domain sparsity with low-rank modeling of RFI, we retrieve the interferogram and reconstruct the SAR image via joint low-rank and sparse optimization. Numerical simulations show that the proposed method can effectively recover SAR images and interferometric phases from RFI-polluted SAR data.

Modern spaceborne synthetic aperture radar (SAR) features a capacity of multiple imaging modes. It comes with Earth-observation data archives consisting of SAR images acquired in various modes with different resolutions and coverage. In this context, in addition to using single-mode images for SAR interferometry (InSAR), exploiting images acquired in different imaging modes for InSAR can provide extra interferograms and, thus, favors the retrieval of interferometric information. The interferometric processing of multimode image pairs requires special considerations due to significant variations in the Doppler spectra. Conventionally, the InSAR technique only uses the spectral band common in both master and slave images, and the remaining band is discarded before interferogram formation. Therefore, conventional processing cannot make full use of the observed data, and the interferogram quality is limited by the common band spectra. In this article, by exploiting the conventionally discarded spectrum, we present a new interferometric phase retrieval method for multimode InSAR data to improve interferogram quality. To this end, first, we propose a linear model to characterize the interferometric phase of a multimode image pair based on image spectral relation. Second, we adopt a sparse recovery method to inverse the linear model for the retrieval of the interferometric phase. Finally, we present real-data experiments on TerraSAR-X staring spotlight to sliding spotlight interferometry and Sentinel-1 strip map to Terrain Observation by Progressive Scan (TOPS) interferometry to test the proposed method. The experiment results show that the proposed method can provide interferograms with reduced phase noise and defocusing effect for multimode InSAR.

As the radio spectrum available to spaceborne synthetic aperture radar (SAR) is restricted to certain limited frequency intervals, there are many different spaceborne SAR systems sharing common frequency bands. Due to this reason, it is reported that two spaceborne SARs at orbit cross positions can potentially cause severe mutual interference. Specifically, the transmitting signal of an SAR, typically linear frequency modulated (LFM), can be directly received by the side or back lobes of another SAR’s antenna, causing radiometric artifacts in the focused image. This article tries to model and characterize the artifacts and study efficient methods for mitigating them. To this end, we formulate an analytical model for describing the artifact, which reveals that the mutual interference can introduce a 2-D LFM radiometric artifact in image domain with a limited spatial extent. We show that the artifact is low-rank based on a range–azimuth decoupling analysis and 2-D high-order Taylor expansion. Based on the low-rank model, we show that two methods, i.e., principal component analysis and its robust variant, can be adopted to efficiently mitigate the artifact via processing in the image domain. The former method has the advantage of fast processing speed, for example, a subswath of Sentinel-1 interferometric wide swath image can be processed within 70 s via blockwise processing, whereas the latter provides improved accuracy for sparse pointlike scatterers. Experiment results demonstrate that the radiometric artifacts caused by mutual interference in Sentinel-1 level-1 images can be efficiently mitigated via the proposed methods.

To avoid decorrelation, conventional synthetic aperture radar interferometry (InSAR) requires that interferometric images should have a common spectral band and the same resolution after proper preprocessing. For a high-resolution (HR) image and a low-resolution (LR) one, the interferogram quality is limited by the LR one since the non-common band (NCB) between two images is usually discarded. In this article, we try to establish an InSAR method to improve interferogram quality by means of exploiting the NCB. To this end, we first define a new interferogram, which has the same resolution as the HR image. Then we formulate the interferometric relationship between the two images into a compressive sensing (CS) model, which contains the proposed HR interferogram. With the sparsity of interferogram in appropriate domains, we model the interferogram formation as a typical sparse recovery problem. Due to the speckle effect in coherent radar imaging, the sensing matrix of our CS model is inherently random. We theoretically prove that the sensing matrix satisfies restricted isometry property, and thus the interferogram recovery performance is guaranteed. Furthermore, we provide a fast interferogram formation algorithm by exploiting computationally efficient structures of the sensing matrix. Numerical experiments show that the proposed method provides better interferogram quality in the sense of reduced phase noise and obtain extrapolated interferogram spectra with respect to CB processing.

This paper presents a quadrature compressive sampling (QuadCS) and associated fast imaging scheme for synthetic aperture radar (SAR). Different from other analog-to-information conversions (AIC), QuadCS AICs using independent spreading signals sample the SAR echoes due to different transmitted pulses. Then the resulting sensing matrix has lower correlation between any two columns than that by a fixed spreading signal, and better SAR image can be reconstructed. With proper setting of the spreading signals in QuadCS, the sensing matrix has the structures suitable for fast computation of matrix-vector multiplication operations, which leads to a fast image reconstruction. The performance of the proposed scheme is assessed using real SAR image. The reconstructed SAR images with only one-fourth of the Nyquist data achieve the image quality similar to that of the classical SAR images with Nyquist samples.

This paper studies the estimation of the delay and Doppler parameters of the sub-Nyquist radars. By formulating the delay-Doppler estimation as the low-rank matrix recovery, we propose an atomic norm minimization-based estimation approach. With the recovered low-rank matrix, we determine and pair the delay and Doppler parameters of the radar targets. Numerical simulations demonstrate the superior performance of the proposed approach, as compared to the state-of-the-art approaches.

Sequential estimation of the delay and Doppler parameters for sub-Nyquist radars by analog-to-information conversion (AIC) systems has received wide attention recently. However, the estimation methods reported are AIC-dependent and have poor performance for off-grid targets. This paper develops a general estimation scheme in the sense that it is applicable to all AICs regardless whether the targets are on or off the grids. The proposed scheme estimates the delay and Doppler parameters sequentially, in which the delay estimation is formulated into a beamspace direction-of- arrival problem and the Doppler estimation is translated into a line spectrum estimation problem. Then the well-known spatial and temporal spectrum estimation techniques are used to provide efficient and high-resolution estimates of the delay and Doppler parameters. In addition, sufficient conditions on the AIC to guarantee the successful estimation of off-grid targets are provided, while the existing conditions are mostly related to the on-grid targets. Theoretical analyses and numerical experiments show the effectiveness and the correctness of the proposed scheme.

For radar echoes sampled at sub-Nyquist rates, it is impractical, if not impossible, to recover full-range Nyquist samples because of huge storage and computational loads. By exploiting the banded structure of the measurement matrix, we develop a novel segment-sliding reconstruction (SegSR) scheme to recover the Nyquist samples through low-cost segment-based computations. An important feature of the proposed SegSR scheme is that the measurement sub-matrix in each segment satisfies the restricted isometry property and thus the recovery performance is guaranteed. Because of the segmenting reconstruction, the adjacent segments will introduce interferences for current segment reconstruction. To reduce the effect of such interference, a two-step orthogonal matching pursuit process (TOMPP) algorithm is proposed for improved segment-based reconstructions. The effectiveness of the proposed SegSR with TOMPP is validated by simulations.

Chaotic compressive sensing is a non‐linear framework for compressive sensing. Along the framework, this study proposes a chaotic analogue‐to‐information converter, ‘chaotic modulation’, to acquire and reconstruct band‐limited sparse analogue signals at sub‐Nyquist rate. In the chaotic modulation, the sparse signal is randomised through state modulation of continuous‐time chaotic system and one state output is sampled as compressive measurements. The reconstruction is achieved through the estimation of the sparse coefficients with the principle of chaotic impulsive synchronisation and l p ‐norm regularised non‐linear least squares. The concept of supreme local Lyapunov exponents (SLLE) is introduced to study the reconstructablity. It is found that the sparse signals are reconstructable, if the largest SLLE of the error dynamic system is negative. As examples, the Lorenz system and the Liu system excited by sparse multi‐tone signals are taken to illustrate the principle and the performance.

This paper is concerned with robust array signal processing in impulsive noise environments. A simple weighting signal is defined to weight all sensor data in a snapshot-by-snapshot way, so that the resulting array data have the desired statistical characteristics used in the subspace-based direction-of-arrival (DOA) estimation techniques. Then any traditional subspace-based technique can be used for DOA estimation. In working example, the MUSIC algorithm is employed and a weighted array data-based MUSIC (WARD-MUSIC) algorithm is detailed. Simulations show the performance advantages of the WARD processing over other related methods in Gaussian mixture noise and symmetric alpha-stable noise