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Editor Work2016 Vol. 5, No. 1
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Sparse signal processing has been utilized to the area of radar sensing. Due to the presence of unknown factors such as the motion of the targets of interest and the error of the radar trajectory, a predesigned dictionary cannot provide the optimally spare representation of the actual radar signals. This paper will introduce a method called parametric sparse representation, which is a special case of dictionary learning and can dynamically learn the unknown factors during the radar sensing and achieve the optimally sparse representation of radar signals. This paper will also introduce the applications of parametric sparse representation to Inverse Synthetic Aperture Radar imaging (ISAR) imaging, Synthetic Aperture Radar imaging (SAR) autofocusing and target recognition based on micro-Doppler effect.
Sparse signal processing has been utilized to the area of radar sensing. Due to the presence of unknown factors such as the motion of the targets of interest and the error of the radar trajectory, a predesigned dictionary cannot provide the optimally spare representation of the actual radar signals. This paper will introduce a method called parametric sparse representation, which is a special case of dictionary learning and can dynamically learn the unknown factors during the radar sensing and achieve the optimally sparse representation of radar signals. This paper will also introduce the applications of parametric sparse representation to Inverse Synthetic Aperture Radar imaging (ISAR) imaging, Synthetic Aperture Radar imaging (SAR) autofocusing and target recognition based on micro-Doppler effect.
2016, 5(1): 8-15.
Optimizing the measurement matrix can improve reconstruction performance in compressed sensing. In this study, we study the measurement matrix optimization method regarding its application to the Two Dictionaries Orthogonal Matching Pursuit (TDOMP) algorithm. The TDOMP is a modified OMP, which uses a matching matrix with low cross-coherence to identify the correct atoms of the sensing matrix. The proposed optimization method is based on alternative projection technique to construct the measurement and matching matrices with low cross-coherence to improve the performance of the TDOMP. Experimental results verify the effectiveness of the proposed method.
Optimizing the measurement matrix can improve reconstruction performance in compressed sensing. In this study, we study the measurement matrix optimization method regarding its application to the Two Dictionaries Orthogonal Matching Pursuit (TDOMP) algorithm. The TDOMP is a modified OMP, which uses a matching matrix with low cross-coherence to identify the correct atoms of the sensing matrix. The proposed optimization method is based on alternative projection technique to construct the measurement and matching matrices with low cross-coherence to improve the performance of the TDOMP. Experimental results verify the effectiveness of the proposed method.
A novel compressed sensing imaging algorithm for high-squint Synthetic Aperture Radar (SAR) based on a Nonlinear Chirp-Scaling (NCS) operator is proposed. First, the echo signal of high-squint SAR is analyzed, and a novel imaging method based on the Nyquist-sampled echo signal is proposed. With the proposed method, the range migration is corrected and the coupling problem in the range and azimuth directions is solved. Then, to solve the problem of high-squint SAR imaging using undersampled echo signals, the NCS operator and compressed sensing algorithm based on this operator are constructed. Imaging results are obtained by solving an optimization problem. The proposed method can recover a sparse scene using undersampled echo data. Furthermore, it can recover a nonsparse scene using fully sampled data. Finally, simulations show the effectiveness of the proposed method.
A novel compressed sensing imaging algorithm for high-squint Synthetic Aperture Radar (SAR) based on a Nonlinear Chirp-Scaling (NCS) operator is proposed. First, the echo signal of high-squint SAR is analyzed, and a novel imaging method based on the Nyquist-sampled echo signal is proposed. With the proposed method, the range migration is corrected and the coupling problem in the range and azimuth directions is solved. Then, to solve the problem of high-squint SAR imaging using undersampled echo signals, the NCS operator and compressed sensing algorithm based on this operator are constructed. Imaging results are obtained by solving an optimization problem. The proposed method can recover a sparse scene using undersampled echo data. Furthermore, it can recover a nonsparse scene using fully sampled data. Finally, simulations show the effectiveness of the proposed method.
2016, 5(1): 25-34.
Sparse microwave imaging is new concept, theory and methodology of microwave imaging, which introduces the sparse signal processing theory to microwave imaging and combines them together to overcome the paradox of increasing system complexity and imaging performance of current Synthetic Aperture Radar (SAR) systems. Traditional airborne SAR systems are facing a phase error problem in the echo which is caused by the non-ideal motion of the aircraft. This phase error could be compensated by autofocus algorithms. But in the sparse microwave imaging, such autofocus algorithm are no longer valid because traditional signal processing based on matched filtering has been replaced with sparse reconstruction. Current autofocus algorithms under sparse constraints are usually based on a two-step iteration, which convergences slowly and costs plenty of computation. In this paper, we introduce the Map-Drift (MD) autofocus algorithm to the accelerated sparse microwave imaging algorithm based on SAR raw data simulator, and propose the novel MD-SAR raw data simulator autofocus algorithm. This algorithm keeps the advantages of both accelerated imaging algorithm and MD algorithm, including the fast convergence and accurate compensation of two-order phase error in echo. Compared with current algorithms based on two-step iteration, the propose method convergences fast and effectively.
Sparse microwave imaging is new concept, theory and methodology of microwave imaging, which introduces the sparse signal processing theory to microwave imaging and combines them together to overcome the paradox of increasing system complexity and imaging performance of current Synthetic Aperture Radar (SAR) systems. Traditional airborne SAR systems are facing a phase error problem in the echo which is caused by the non-ideal motion of the aircraft. This phase error could be compensated by autofocus algorithms. But in the sparse microwave imaging, such autofocus algorithm are no longer valid because traditional signal processing based on matched filtering has been replaced with sparse reconstruction. Current autofocus algorithms under sparse constraints are usually based on a two-step iteration, which convergences slowly and costs plenty of computation. In this paper, we introduce the Map-Drift (MD) autofocus algorithm to the accelerated sparse microwave imaging algorithm based on SAR raw data simulator, and propose the novel MD-SAR raw data simulator autofocus algorithm. This algorithm keeps the advantages of both accelerated imaging algorithm and MD algorithm, including the fast convergence and accurate compensation of two-order phase error in echo. Compared with current algorithms based on two-step iteration, the propose method convergences fast and effectively.
2016, 5(1): 35-41.
Azimuth ambiguities appear widely throughout spaceborne Synthetic Aperture Radar (SAR) images. If the ambiguous energy is relatively strong, a large number of brilliant areas or points will emerge, which may be erroneously judged as actual targets. This is a disadvantage in image interpretation. Due to the fact that ambiguous energy is mixed with energy from the main zone in the frequency and time domains, it is difficult to suppress azimuth ambiguity to a reasonable level using the existing approach without loss of resolution. This study proposes an innovative approach for suppressing azimuth ambiguity based on the compressive sensing recovery framework, in which the original image acts as prior information and the corresponding frequency spectrum truncated in a proper ratio acts as measurement information. With the proposed approach, highresolution low-ambiguity images can be obtained by iteration. We used simulation and satellite data to validate the effectiveness of this proposed approach in suppressing azimuth ambiguity.
Azimuth ambiguities appear widely throughout spaceborne Synthetic Aperture Radar (SAR) images. If the ambiguous energy is relatively strong, a large number of brilliant areas or points will emerge, which may be erroneously judged as actual targets. This is a disadvantage in image interpretation. Due to the fact that ambiguous energy is mixed with energy from the main zone in the frequency and time domains, it is difficult to suppress azimuth ambiguity to a reasonable level using the existing approach without loss of resolution. This study proposes an innovative approach for suppressing azimuth ambiguity based on the compressive sensing recovery framework, in which the original image acts as prior information and the corresponding frequency spectrum truncated in a proper ratio acts as measurement information. With the proposed approach, highresolution low-ambiguity images can be obtained by iteration. We used simulation and satellite data to validate the effectiveness of this proposed approach in suppressing azimuth ambiguity.
2016, 5(1): 42-56.
Sparse microwave imaging using sparse priors of observed scenes in space, time, frequency, or polarization domain and echo data with sampling rate smaller than the traditional Nyquist rate as well as optimization algorithms for reconstructing the microwave images of observed scenes has many advantages over traditional microwave imaging systems. In sparse microwave imaging, image acquisition and representation vary; therefore, new feature analysis and cognitive interpretation theories and methods should be developed based on current research results. In this study, we analyze the statistical properties of sparse Synthetic Aperture Radar (SAR) images and changes in point, line and regional features induced by sparse reconstruction. For SAR images recovered by the spatial sparse model, the statistical distribution degrades, whereas points and lines can be accurately extracted by low sampling rates. Furthermore, the target detection method based on sparse SAR images is studied. Owing to a weak background noise, target detection is easier using sparse SAR images than traditional ones.
Sparse microwave imaging using sparse priors of observed scenes in space, time, frequency, or polarization domain and echo data with sampling rate smaller than the traditional Nyquist rate as well as optimization algorithms for reconstructing the microwave images of observed scenes has many advantages over traditional microwave imaging systems. In sparse microwave imaging, image acquisition and representation vary; therefore, new feature analysis and cognitive interpretation theories and methods should be developed based on current research results. In this study, we analyze the statistical properties of sparse Synthetic Aperture Radar (SAR) images and changes in point, line and regional features induced by sparse reconstruction. For SAR images recovered by the spatial sparse model, the statistical distribution degrades, whereas points and lines can be accurately extracted by low sampling rates. Furthermore, the target detection method based on sparse SAR images is studied. Owing to a weak background noise, target detection is easier using sparse SAR images than traditional ones.
2016, 5(1): 57-64.
While the use of SAR Tomography (TomoSAR) based on Compressive Sensing (CS) makes it possible to reconstruct the height profile of an observed scene, the performance of the reconstruction decreases for a structural observed scene. To deal with this issue, we propose using TomoSAR based on Block Compressive Sensing (BCS), which changes the reconstruction of the structural observed scene into a BCS problem under the principles of CS. Further, the block size is established by utilizing the relationship between the characteristics of the structural observed scene and the SAR parameters, such that the BCS problem is efficiently solved with a block sparse l1/l2 norm optimization signal model. Compared with existing CSTomoSAR methods, the proposed BCS-TomoSAR method makes better use of the sparsity and structure information of a structural observed scene, and has higher precision and better reconstruction performance. We used simulations and Radarsat-2 data to verify the effectiveness of this proposed method.
While the use of SAR Tomography (TomoSAR) based on Compressive Sensing (CS) makes it possible to reconstruct the height profile of an observed scene, the performance of the reconstruction decreases for a structural observed scene. To deal with this issue, we propose using TomoSAR based on Block Compressive Sensing (BCS), which changes the reconstruction of the structural observed scene into a BCS problem under the principles of CS. Further, the block size is established by utilizing the relationship between the characteristics of the structural observed scene and the SAR parameters, such that the BCS problem is efficiently solved with a block sparse l1/l2 norm optimization signal model. Compared with existing CSTomoSAR methods, the proposed BCS-TomoSAR method makes better use of the sparsity and structure information of a structural observed scene, and has higher precision and better reconstruction performance. We used simulations and Radarsat-2 data to verify the effectiveness of this proposed method.
2016, 5(1): 65-71.
Observation data obtained from the Four-Dimensional (4D) Synthetic Aperture Radar (SAR) system is sparse and non-uniform in the baseline-time plane. Hence, the imaging results acquired by traditional Fourier-based methods are limited by high side lobes. Compressive Sensing (CS) is a recently proposed technique that allows for the recovery of an unknown sparse signal with overwhelming probability from very limited samples. However, the standard CS framework has been developed for real-valued signals, and the imaging process for 4D synthetic aperture radar deals with complex-valued data. In this study, we propose a new 4D synthetic aperture radar imaging algorithm based on an iterative reconstruction of magnitude and phase, which transforms the height-velocity imaging problem of 4D synthetic aperture radar into a joint reconstruction problem of the magnitude and phase of the complex-valued scatter coefficient. Using the phase information in the algorithm, the image quality is improved. Simulation results confirm the effectiveness of the proposed method.
Observation data obtained from the Four-Dimensional (4D) Synthetic Aperture Radar (SAR) system is sparse and non-uniform in the baseline-time plane. Hence, the imaging results acquired by traditional Fourier-based methods are limited by high side lobes. Compressive Sensing (CS) is a recently proposed technique that allows for the recovery of an unknown sparse signal with overwhelming probability from very limited samples. However, the standard CS framework has been developed for real-valued signals, and the imaging process for 4D synthetic aperture radar deals with complex-valued data. In this study, we propose a new 4D synthetic aperture radar imaging algorithm based on an iterative reconstruction of magnitude and phase, which transforms the height-velocity imaging problem of 4D synthetic aperture radar into a joint reconstruction problem of the magnitude and phase of the complex-valued scatter coefficient. Using the phase information in the algorithm, the image quality is improved. Simulation results confirm the effectiveness of the proposed method.
2016, 5(1): 72-81.
Orthogonal Frequency Division Multiplexing (OFDM) technology has been utilized in radar imaging to obtain high-resolution range profiles without inter-range cell interference. In this study, we establish a novel algorithm for Inverse Synthetic Aperture Radar (ISAR) imaging of a non-cooperative target using OFDM waveforms. We also achieve motion compensation and image enhancement with sparse reconstruction optimization. Utilizing sparse reconstruction optimization, we can simultaneously achieve high-precision OFDM-ISAR imaging and also correct phase errors. Extensive experimentation confirms that the proposed method can effectively overcome range interference and phase errors in OFDM-ISAR imaging, providing optimal robustness and precision.
Orthogonal Frequency Division Multiplexing (OFDM) technology has been utilized in radar imaging to obtain high-resolution range profiles without inter-range cell interference. In this study, we establish a novel algorithm for Inverse Synthetic Aperture Radar (ISAR) imaging of a non-cooperative target using OFDM waveforms. We also achieve motion compensation and image enhancement with sparse reconstruction optimization. Utilizing sparse reconstruction optimization, we can simultaneously achieve high-precision OFDM-ISAR imaging and also correct phase errors. Extensive experimentation confirms that the proposed method can effectively overcome range interference and phase errors in OFDM-ISAR imaging, providing optimal robustness and precision.
2016, 5(1): 82-89.
Space group debris imaging is difficult with sparse data in low Pulse Repetition Frequency (PRF) spaceborne radar. To solve this problem in the narrow band system, we propose a method for space group debris imaging based on sparse samples. Due to the diversity of mass, density, and other factors, space group debris typically rotates at a high speed in different ways. We can obtain angular velocity through the autocorrelation function based on the diversity in the angular velocity. The scattering field usually presents strong sparsity, so we can utilize the corresponding measurement matrix to extract the data of different debris and then combine it using the sparse method to reconstruct the image. Furthermore, we can solve the Doppler ambiguity with the measurement matrix in low PRF systems and suppress some energy of other debris. Theoretical analysis confirms the validity of this methodology. Our simulation results demonstrate that the proposed method can achieve high-resolution Inverse Synthetic Aperture Radar (ISAR) images of space group debris in low PRF systems.
Space group debris imaging is difficult with sparse data in low Pulse Repetition Frequency (PRF) spaceborne radar. To solve this problem in the narrow band system, we propose a method for space group debris imaging based on sparse samples. Due to the diversity of mass, density, and other factors, space group debris typically rotates at a high speed in different ways. We can obtain angular velocity through the autocorrelation function based on the diversity in the angular velocity. The scattering field usually presents strong sparsity, so we can utilize the corresponding measurement matrix to extract the data of different debris and then combine it using the sparse method to reconstruct the image. Furthermore, we can solve the Doppler ambiguity with the measurement matrix in low PRF systems and suppress some energy of other debris. Theoretical analysis confirms the validity of this methodology. Our simulation results demonstrate that the proposed method can achieve high-resolution Inverse Synthetic Aperture Radar (ISAR) images of space group debris in low PRF systems.
2016, 5(1): 90-98.
A multiple targets cognitive radar tracking method based on Compressed Sensing (CS) is proposed. In this method, the theory of CS is introduced to the case of cognitive radar tracking process in multiple targets scenario. The echo signal is sparsely expressed. The designs of sparse matrix and measurement matrix are accomplished by expressing the echo signal sparsely, and subsequently, the restruction of measurement signal under the down-sampling condition is realized. On the receiving end, after considering that the problems that traditional particle filter suffers from degeneracy, and require a large number of particles, the particle swarm optimization particle filter is used to track the targets. On the transmitting end, the Posterior Cramr-Rao Bounds (PCRB) of the tracking accuracy is deduced, and the radar waveform parameters are further cognitively designed using PCRB. Simulation results show that the proposed method can not only reduce the data quantity, but also provide a better tracking performance compared with traditional method.
A multiple targets cognitive radar tracking method based on Compressed Sensing (CS) is proposed. In this method, the theory of CS is introduced to the case of cognitive radar tracking process in multiple targets scenario. The echo signal is sparsely expressed. The designs of sparse matrix and measurement matrix are accomplished by expressing the echo signal sparsely, and subsequently, the restruction of measurement signal under the down-sampling condition is realized. On the receiving end, after considering that the problems that traditional particle filter suffers from degeneracy, and require a large number of particles, the particle swarm optimization particle filter is used to track the targets. On the transmitting end, the Posterior Cramr-Rao Bounds (PCRB) of the tracking accuracy is deduced, and the radar waveform parameters are further cognitively designed using PCRB. Simulation results show that the proposed method can not only reduce the data quantity, but also provide a better tracking performance compared with traditional method.
2016, 5(1): 99-108.
Nowadays, high-speed sampling and transmission is a foremost challenge of radar system. In order to solve this problem, a compressive sensing approach is proposed for radar target signals in this study. Considering the block sparse structure of signals, the proposed method uses a simple measurement matrix to sample the signals and employ a Block Sparse Bayesian Learning (BSBL) algorithm to recover the signals. The classical BSBL algorithm is applicable to real signal, while radar signals are complex. Therefore, a Complex Block Sparse Bayesian Learning (CBSBL) is extended for the radar target signal reconstruction. Since the existed radar signal compressive sensing models do not take block structures in consideration, the signal reconstruction of proposed approach is more accurate and robust, and the simple measurement matrix leads to an easy implementation of hardware. The effectiveness of the proposed approach is demonstrated by numerical simulations.
Nowadays, high-speed sampling and transmission is a foremost challenge of radar system. In order to solve this problem, a compressive sensing approach is proposed for radar target signals in this study. Considering the block sparse structure of signals, the proposed method uses a simple measurement matrix to sample the signals and employ a Block Sparse Bayesian Learning (BSBL) algorithm to recover the signals. The classical BSBL algorithm is applicable to real signal, while radar signals are complex. Therefore, a Complex Block Sparse Bayesian Learning (CBSBL) is extended for the radar target signal reconstruction. Since the existed radar signal compressive sensing models do not take block structures in consideration, the signal reconstruction of proposed approach is more accurate and robust, and the simple measurement matrix leads to an easy implementation of hardware. The effectiveness of the proposed approach is demonstrated by numerical simulations.
2016, 5(1): 109-117.
A conformal sparse array based on combined Barker code is designed for airship platform. The performance of the designed array such as signal-to-noise ratio is analyzed. Using the hovering characteristics of the airship, interferometry operation can be applied on the real aperture imaging results of two pulses, which can eliminate the random backscatter phase and make the image sparse in the transform domain. Building the relationship between echo and transform coefficients, the Compressed Sensing (CS) theory can be introduced to solve the formula and achieving imaging. The image quality of the proposed method can reach the image formed by the full array imaging. The simulation results show the effectiveness of the proposed method.
A conformal sparse array based on combined Barker code is designed for airship platform. The performance of the designed array such as signal-to-noise ratio is analyzed. Using the hovering characteristics of the airship, interferometry operation can be applied on the real aperture imaging results of two pulses, which can eliminate the random backscatter phase and make the image sparse in the transform domain. Building the relationship between echo and transform coefficients, the Compressed Sensing (CS) theory can be introduced to solve the formula and achieving imaging. The image quality of the proposed method can reach the image formed by the full array imaging. The simulation results show the effectiveness of the proposed method.
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