Compressive SAR Imaging of Moving Targets

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SAR Imaging of Moving Targets via Compressive Sensing

Jun Wang, Gang Li, Hao Zhang, Xiqin Wang

An algorithm based on compressive sensing (CS) is proposed for synthetic aperture radar (SAR) imaging of moving targets. The received SAR echo is decomposed into the sum of basis sub-signals, which are generated by discretizing the target spatial domain and velocity domain and synthesizing the SAR received data for every discretized spatial position and velocity candidate. In this way, the SAR imaging problem is converted into sub-signal selection problem. In the case that moving targets are sparsely distributed in the observed scene, their reflectivities, positions and velocities can be obtained by using the CS technique. It is shown that, compared with traditional algorithms, the target image obtained by the proposed algorithm has higher resolution and lower side-lobe while the required number of measurements can be an order of magnitude less than that by sampling at Nyquist sampling rate. Moreover, multiple targets with different speeds can be imaged simultaneously, so the proposed algorithm has higher efficiency. 

Abstract

An algorithm based on compressive sensing (CS) is proposed for synthetic aperture radar (SAR) imaging of moving targets. The received SAR echo is decomposed into the sum of basis sub-signals, which are generated by discretizing the target spatial domain and velocity domain and synthesizing the SAR received data for every discretized spatial position and velocity candidate. In this way, the SAR imaging problem is converted into sub-signal selection problem. In the case that moving targets are sparsely distributed in the observed scene, their reflectivities, positions and velocities can be obtained by using the CS technique. It is shown that, compared with traditional algorithms, the target image obtained by the proposed algorithm has higher resolution and lower side-lobe while the required number of measurements can be an order of magnitude less than that by sampling at Nyquist sampling rate. Moreover, multiple targets with different speeds can be imaged simultaneously, so the proposed algorithm has higher efficiency.

Synthetic aperture radar (SAR) has been widely used for stationary scene imaging via matched filtering and discrete Fourier transform (DFT). Recently, moving target imaging has attracted much attention. However, the image of moving targets in the observed scene may be displaced and blurred in the azimuth direction because of the motion of targets. Many algorithms have been proposed to deal with this problem. One class of algorithms is based on the estimation of target motion parameters [1-9], e.g., the Doppler rate and the Doppler frequency centroid which are related to the velocities along the range and azimuth directions, respectively. Another class of algorithms combines data reformatting with high order Doppler history analysis, i.e., the Keystone transform [10], the second Keystone transform [11] or the Doppler Keystone transform [12] is used to correct the range cell migration of target, and then the time-frequency analysis [20] or polynomial phase analysis is used to compensate the high order terms in the Doppler history. All the algorithms above convert moving target imaging problem to static target imaging problem by compensating the error caused by the target motion, and then the algorithms for stationary scene imaging, e.g., the Range- Doppler algorithm, can be used for imagery formation. Since the Range-Doppler algorithm is based on matched filtering and DFT, the resolutions of final image in the range and azimuth directions are limited by the bandwidth of transmitted signal and the length of the synthetic aperture, respectively. And high side-lobes arise due to the DFT window effect. Moreover, the required Nyquist-rate sampling may cause huge data amount to achieve high resolution. In addition, in above algorithms it is needed to deal with different targets respectively when there are multiple targets with different speeds.

Recently, the compressive sensing (CS) theory [13-15] has been used in a variety of areas for its excellent performance on reconstruction of sparse signals. Consider an equation y = Φx , where x is an unknown k-sparse signal of length N (k-sparse means that x has k large elements), Φ is a M  N measurement matrix, and y is the measurement vector of length M . The CS theory states that x can be reconstructed by M  O(k log N ) measurements with high probability [13-15].

CS has already been applied to SAR imaging of static targets [16-18]. However, the algorithms in [16-18] are not suitable for SAR imaging of moving targets due to the motion-induced phase error.

In this paper, we propose an algorithm of SAR imaging of moving targets based on the CS technique. We use the matching pursuit strategy to formulate the SAR imaging problem as a basis sub-signal selection problem, where the basis sub-signals are produced by discretizing the extended target space (here the extended target space is defined as a four-dimensional domain spanned by range and azimuth positions and range and azimuth velocities) and synthesizing the SAR data for every discretized spatial position and velocity candidate in the extended target space. There are two assumptions we make here. First, all targets maintain uniform motion in the observation time. Second, the discretized target space is sparse, i.e., the number of targets is much less than the size of discretized target space. By using the CS technique, the spatial positions and the velocities of the targets can be reconstructed with a relatively small number of random measurements. Compared with traditional DFT-based algorithms of moving target imaging, the proposed algorithm can obtain higher resolution and lower side-lobe with fewer measurements. Moreover, multiple targets with different speeds can be simultaneously imaged by using our algorithm and thus the imaging efficiency can be improved.

Comments: 13 pages, 4 figures
Subjects: Information Theory (cs.IT)
Cite as: arXiv:1104.1074 [cs.IT]
(or arXiv:1104.1074v1 [cs.IT] for this version)
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