Abstract
Compressive radar imaging has attracted considerable attention because it substantially reduces imaging time through directly compressive sampling. However, a problem that must be addressed for compressive radar imaging systems is the high computational complexity of reconstruction of sparse signals. In this paper, a novel algorithm, called two-dimensional (2D) normalized iterative hard thresholding (NIHT) or 2D-NIHT algorithm, is proposed to directly reconstruct radar images in the matrix domain. The reconstruction performance of 2D-NIHT algorithm was validated by an experiment on recovering a synthetic 2D sparse signal, and the superiority of the 2D-NIHT algorithm to the NIHT algorithm was demonstrated by a comprehensive comparison of its reconstruction performance. Moreover, to be used in compressive radar imaging systems, a 2D sampling model was also proposed to compress the range and azimuth data simultaneously. The practical application of the 2D-NIHT algorithm in radar systems was validated by recovering two radar scenes with noise at different signal-to-noise ratios, and the results showed that the 2D-NIHT algorithm could reconstruct radar scenes with a high probability of exact recovery in the matrix domain. In addition, the reconstruction performance of the 2D-NIHT algorithm was compared with four existing efficient reconstruction algorithms using the two radar scenes, and the results illustrated that, compared to the other algorithms, the 2D-NIHT algorithm could dramatically reduce the computational complexity in signal reconstruction and successfully reconstruct 2D sparse images with a high probability of exact recovery.
Highlights
Radar, an object detection system using radio waves to detect objects and determine their spatial positions, has been applied in many fields, including radar astronomy, geographical environment surveillance system, and air defense systems
On the one hand, an experiment with syncretic sparse images was conducted to demonstrate the feasibility of the 2D-normalized iterative hard thresholding (NIHT) algorithm and its superiority to the NIHT algorithm in reconstruction time
It was obvious that the reconstructed image using the 2D-NIHT algorithm was clean without any noise, because the nonlinear operation process of K [X ] in the 2D-NIHT algorithm was capable of setting N1 × N2 − K elements of X
Summary
An object detection system using radio waves to detect objects and determine their spatial positions, has been applied in many fields, including radar astronomy, geographical environment surveillance system, and air defense systems. Classical time–frequency uncertainty principles based on the Shannon sampling theorem have limited the development of high-resolution and high–speed radar imaging [1]. Braniuk and co-workers first applied the compressive sensing theorem in radar imaging systems and confirmed the feasibility of compressive radar imaging by theoretical analysis and numerical experiments [3]. Zhang and co-workers proposed a framework to realize high–resolution inverse synthetic aperture radar (ISAR) imaging with limited measured data based on the theory of compressed sampling [4]. An approach that employed pulse accumulation and weighted compressive sensing was proposed by Zhang and co-workers under low signal-to-noise ratio (SNR) conditions, to realize high-resolution imaging and reduce sensitivity to noise [10]. Xie and co-workers proposed a smoothed L0 norm (SL0) algorithm to obtain fast radar imaging based on a compressive sensing [11]; Bhattacharya and co-workers used convex optimization through projection onto convex sets or greedy algorithms to decode compressive synthetic aperture radar (SAR) images [12,13]; and Yu and co-workers introduced a turbo-like iterative thresholding algorithm to recover SAR images [14]
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