In this paper, a SAR imagery compressing and reconstruction method based on Compressed Sensing (CS) theory is proposed. In the method, the SAR imagery can be divided to several sub-imageries firstly. Discrete Wavelet Transform (DWT) can be utilized to make SAR imagery sparse and the random Gauss matrix after approximate Orthogonal-matrix and Right-matrix (QR) decomposition can be employed to complete the low-dimension measurement for sparse results. For reconstructing SAR imagery, a modified Orthogonal Matching Pursuit (OMP) algorithm is proposed to perform better. On condition of the same reconstruction precision, the search burden is reduced and convergency speed is enhanced by using the proposed modified OMP algorithm. At the same time, the sparsity estimation can be avoided. Furthermore, some processing containing IDWT can be engaged to achieve the final reconstructed SAR imagery. The effectiveness of the proposed method can be validated by simulation results.
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