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This paper proposes a new compression framework for SAR images. A maximum a posteriori (MAP) estimator is first utilized for despeckling, and by using total variation (TV), the denoised SAR image is decomposed into structure and texture. Such two components undergo discrete wavelet transform and wavelet packet transform, respectively. And then, according to their unique characteristics, two different wavelet coding algorithms are presented to encode the respective component. Experimental results shown that the reconstructed image has good visual quality and the peak signal-to-noise ratio (PSNR) is excellent.