Accurate imputation of missing data is crucial in the Industrial Internet-of-Things (IIoT), where operations are often compromised by noisy samples from harsh environments. Traditional imputation methods struggle with such noise due to their black-box nature or lack of adaptability. To address this issue, we recast data imputation as a distribution alignment challenge, utilizing the flexibility of optimal transport (OT) to handle noisy samples. Specifically, we first introduce the Proximal Optimal Transport (POT) problem, where the transportation cost is obtained by the network simplex approach with a selective matching mechanism, which renders it capable of matching distributions with noisy samples. Subsequently, we propose the POT-I framework, where the objective is to minimize the transport cost of POT. The produced gradient is used to refine the imputation value, which achieves missing data imputation (MDI) while getting robustness to noisy samples. Experiments on real-world IIoT datasets demonstrate the superiority of POT-I over state-of-the-art imputation methods.

As a novel configuration of along-track Multistatic SAR (Multi-SAR), the high frame rate Along-Track Swarm SAR (ATS-SAR) has garnered significant attention in recent years due to its exceptional efficiency in reducing data acquisition time. Motivated by its potential for high-resolution imaging of moving targets, this paper investigates the application of ATS-SAR in moving target imaging. However, high frame rate ATS-SAR-based moving target imaging confronts two critical challenges: time-space coupling and partial data loss in moving target echoes. To address these challenges, we first conduct a comprehensive analysis and theoretical derivation of the moving target echo model under the high frame rate ATS-SAR configuration. Subsequently, we propose an innovative motion parameter estimation algorithm that exploits unique echo characteristics to achieve high-performance imaging. Furthermore, we introduce the highresolution, high frame rate ATS-SAR Sub-Aperture Collaborative Imaging algorithm for Moving Targets (MT-SACIm-ATS). Extensive simulations and a real measured experiment validate the effectiveness of the MT-SACIm-ATS algorithm, demonstrating imaging performance that closely approximates reference imaging results. Comparative analysis with several state-of-the-art algorithms further highlights the superiority of the proposed approach in terms of resolution and robustness.

For airborne synthetic aperture radar (SAR) imaging with high resolution and wide swath, the atmospheric turbulence may produce serious range-dependent (RD) motion error. To estimate the RD motion error, traditional methods usually first divide the range full-aperture data into multiple range blocks, and then use phase gradient autofocus (PGA) to estimate the phase error of all range blocks one by one, which is inefficient. In addition, the robustness of PGA is also affected by the number of strong scattering points. To solve these two problems, a new motion compensation (MoCo) algorithm is proposed to improve the efficiency and robustness of airborne SAR MoCo. The real data-processing results are given to verify the effectiveness of the algorithm.

Synthetic aperture radar (SAR) imaging usually needs to be converted between the time domain and the frequency domain, in which the solution of stationary phase point determines the accuracy of time–frequency conversion and the final image quality. Theoretically, the stationary phase point can be accurately solved by the method of series reversion (MSR) in an arbitrary configuration (e.g., bistatic and/or nonlinear trajectory). However, the existing methods based on MSR are proposed based on the assumption of specific signal form. In other words, it is necessary to reuse MSR to derive the time–frequency conversion for different signal forms, which brings great inconvenience to engineering applications. In this article, we aim to propose a general method based on MSR. Based on this method, the accurate time–frequency conversion can be derived by simply arranging any signal to the standard form specified in this article first and then simply replacing the variables.

Due to the requirements of portability and omni-directivity, the planar bow-tie antenna is widely used in impulse through-wall radar (ITWR). When the planar bow-tie antenna is used to radiate the ultrawide bandwidth (UWB) signal, the ringing phenomenon of the transmitted signal would be serious, which can damage the quality of radar imaging. The previous solutions for this problem are the usage of various hardware loadings; however, those loadings could cause signal energy loss and reduce the signal gain. Alternatively, this letter studies a deconvolution-technique-based signal processing approach to suppress the signal ringing. Because the proposed approach does not require any hardware loadings on the antenna, it can help improve the signal-to-noise ratio (SNR) and significantly reduce the energy loss of signal. The effectivity of this signal processing approach is verified by the radar detecting experiments.

Squint ultrahigh-resolution (UHR) synthetic aperture radar (SAR) generally uses the extended Omega-K algorithm (EOK) for range cell migration correction (RCMC). However, the extra range migration and defocusing (ERMD) will be introduced by the EOK when there are motion errors. This problem will be severe as the squint angle increases, which may sharply reduce the signal-to-noise ratio (SNR) and lead to the failure of the existing autofocus methods. In this letter, a UHR autofocus algorithm based on cascaded map-drift (MD)-PGA is proposed. The MD is used for the rough estimation to improve the SNR and the phase gradient algorithm (PGA) is used to accurately estimate the residual error based on a relatively high SNR. The new algorithm combines the advantages of MD and PGA, which can solve the problem of severe defocusing. The processing of airborne real data validates the effectiveness of the proposed algorithm.

Spaceborne synthetic aperture radar (SAR) real-time imaging is especially important for disaster emergencies and real-time monitoring applications with highly desired real-time requirements. Therefore, the continuous improvement of real-time imaging efficiency is an important development trend. At present, traditional real-time imaging algorithms based on constant pulse repetition frequency (PRF) have low accuracy when processing spaceborne SAR data with nonlinear trajectory. For this problem, the existing methods usually introduce some complex signal processing steps, such as scaling or interpolation processing, to improve the accuracy of the real-time imaging, but this will reduce its efficiency. Therefore, this article proposes a new real-time imaging algorithm based on variable PRF for nonlinear trajectory spaceborne SAR. By introducing the variable PRF, the proposed algorithm is equivalent to complete the complex signal processing steps in the radar signal transmission stage, which can greatly improve the efficiency of real-time imaging. Simulation experiments verify the effectiveness of the algorithm.

Division-of-focal-plane (DoFP) polarimeter provides a way for snapshot acquisition, making it available to simultaneously record polarization measurements at different orientations. This polarization imaging system has gained more attention in the last few years and is promising to be used in the fields of computer vision and remote sensing. However, this system suffers from the degradation of spatial resolution. To reconstruct polarization information at full resolution, polarization image demosaicking is indispensable. To address polarization image demosaicking issue while preserving the essential structure of polarization data, a sparse tensor factorization-based model is proposed. For a target cube, its similar cubes are first grouped together as a tensor. Then, its compact dictionary and sparse core tensor are learned by factorizing the tensor using sparse coding. Moreover, the correlation among different polarization orientations and the nonlocal self-similarity are adopted to boost the performance. Experimental results on synthetic and real-world data demonstrate that our proposed model outperforms several state-of-the-art methods in terms of both quantitative measurements and visual quality.

A nonlinear trajectory of a radar platform in synthetic aperture radar (SAR) may lead to severe coupling between the range and the azimuth, which may make the ambiguity function (AF) analysis complicated. The numerical algorithm-based AF analysis may be computationally expensive, while the existing analytical algorithm-based AF analysis may cause large errors because it does not consider the coupling between the range and the azimuth. By observing that the singular value decomposition (SVD) is good to deal with the coupling problem, in this article, we propose an effective AF analysis based on SVD. The key idea is to first use a small amount of sampling points for SVD of the coupled term in the AF and then the decoupled vectors are fitted to high-order polynomials for the analytical AF calculation. It converts the double integral into the product of two single integrals in the calculation. From the proposed SVD-based AF analysis, three parameters, namely, 3-dB resolution, peak sidelobe ratio (PSLR), and integrated sidelobe ratio (ISLR), are then effectively computed. The simulated results verify the good performance of the proposed SVD-based AF analysis.

For the airborne SAR imaging, the motion compensation (MOCO) is required because of the phase error caused by the atmospheric turbulence. In the case of ultrahigh-resolution and wide-swath, the phase error may be rangedependent (RD), which may induce a RD residual-RCM after the correction of range cell migration (RCM) by using the range migration algorithm (RMA). Currently, phase gradient autofocus (PGA) is widely used to estimate the phase error from the raw data. However, the RD residual-RCM may degrade the accuracy of the PGA. To overcome such a problem, we present a CZT correction algorithm to correct the RD residual-RCM. Processing of airborne real data validates the effectiveness of the proposed algorithm.

The motion compensation (MOCO) for the airborne SAR with ultrahigh resolution and wide swath is required to consider the range-dependent (RD) phase error. The RD phase error may cause an RD residual-range cell migration (RCM) after the correction of RCM, which can degrade the performance of phase gradient autofocus (PGA) when estimating the phase error. In addition, because the PGA estimation is based on the strong scattering point, it may wrongly estimate the phase error for some observation scenes without strong scattering point. Alternatively, to take into account the above two problems, we study a MOCO algorithm based on two-step accuracy improvement. In the algorithm, the first step is to estimate and correct the RD residual-RCM and thus improves the accuracy of PGA. The second step is to develop a prior-information-based-weighted least square (PI-WLS) to further improve the accuracy of RD phase error estimation. Processing of airborne real data validates the effectiveness of the proposed algorithm.

The curved trajectory can lead to severely 2-D spatial-variance in spaceborne synthetic aperture radar (SAR). The azimuth-variance makes the traditional frequency domain imaging algorithms for the straight trajectory based on the assumption of azimuth translational invariance invalid. To correct the severely 2-D spatial-variance in curved trajectory spaceborne SAR, this paper studies a frequency imaging algorithm based on an optimal linear range walk correction (LRWC) preprocessing and 2-D singular value decomposition (SVD). Before the correction of the 2-D spatial-variance, an optimal LRWC preprocessing is introduced to minimize the azimuth-variance. Subsequently, a range block-SVD is proposed to correct the range-variance and, thus, achieves the accurate range cell migration correction. Finally, the azimuth tandem-SVD method is used to correct the azimuth-variance and, thus, accomplishes the azimuth compression for the whole azimuth scene. Processing of the simulated data validates the effectiveness of the proposed algorithm.