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Synthetic aperture radar (SAR) images suffer from speckle noise that degrades image quality. Also, speckle removal is needed for lossy image compression as such noise increases image entropy. Nevertheless, most lossy compression schemes act as lowpass filters that might not suit multiplicative noise reduction. In order to build a compression scheme that takes into consideration statistics of SAR images, a well-known reflectivity estimator is integrated into an JPEG 2000-like image compression strategy, so that image compression artifacts may be viewed as an adaptive despeckle filter instead of a simple lowpass filter. It yields a compression algorithm that acts in a similar way to the Lee (or Kuan) filter.