In this paper, we consider the optimization of measurement matrix in Compressed Sensing (CS) framework. Based on the boundary constraint, we propose a novel algorithm to make the “mutual coherence” approach a lower bound. This algorithm is implemented by using an iterative strategy. In each iteration, a neighborhood interval of the maximal off-diagonal entry in the Gram matrix is scaled down with the same shrinkage factor, and then a lower mutual coherence between the measurement matrix and sparsifying matrix is obtained. After many iterations, the magnitudes of most of off-diagonal entries approach the lower bound. The proposed optimization algorithm demonstrates better performance compared with other typical optimization methods, such as t-averaged mutual coherence. In addition, the effectiveness of CS can be used for the compression of complex synthetic aperture radar (SAR) image is verified, and experimental results using simulated data and real field data corroborate this claim.

In this paper, a new scheme is presented for ground moving target indication for multichannel high-resolution wide-swath (HRWS) SAR systems with modified reconstruction filters. The conventional steering vector is generalized for moving targets through taking into account the additional Doppler centroid shift caused by the across-track velocity. Two modified steering vectors with symmetric velocity information are utilized to produce two images for the same scene. Due to the unmatched steering vectors, the stationary backgrounds are defocused but they still hold the same intensities in both images but moving targets are blurred to different extents. The ambiguous components of the moving targets can also be suppressed due to the beamforming in the reconstruction procedure. Therefore, ground moving target indication can be carried out via intensity comparison between the two images. The effectiveness of the proposed method is verified by both simulated and real airborne SAR data.

The classification of warheads and decoys is a core technology in the defense of the ballistic missile. Usually, a high range resolution is favorable for the development of the classification algorithm, which requires a high sampling rate in fast time, and thus leads to a heavy computation burden for data processing. In this paper, a novel method based on compressed sensing (CS) is presented to improve the range resolution of the target with low computational complexity. First, a tool for electromagnetic calculation, such as CST Microwave Studio, is used to simulate the frequency response of the electromagnetic scattering of the target. Second, the range-resolved signal of the target is acquired by further processing. Third, a greedy algorithm is applied to this signal. By the iterative search of the maximum value from the signal rather than the calculation of the inner product for raw echo, the scattering coefficients of the target can be reconstructed efficiently. A series of experimental results demonstrates the effectiveness of our method.

In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.