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.

Synthetic aperture radar (SAR) image generation is crucial to SAR image interpretation when sufficient image samples are unavailable. Against this background, a method for SAR image generation of three-dimensional (3D) target is proposed in this paper. Specifically, this method contains three steps. Firstly, according to the system parameters, the echo signal in the two-dimensional (2D) time domain is generated, based on which 2D Fast Fourier Transform (2DFFT) is performed. Secondly, the hybrid moments (MoM)-large element physical optics (LEPO) method is used to calculate the scattering characteristics with the certain frequency points and incident angles according to the system parameters. Finally, range Doppler algorithm (RDA) is adopted to process the signal in the 2D-frequency domain with radar cross section (RCS) exported from electromagnetic calculations. These procedures combine RCS computations by FKEO solver and RDA to simulate raw echo signal and then generate SAR image samples for different squint angles and targets with reduced computational load, laying foundations for transmit waveform design, SAR image interpretation and other SAR related work.

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.