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In this letter, we focus on a new compression scheme for synthetic aperture radar (SAR) amplitude images. The last decade has seen a growing interest in the study of dictionary learning and sparse representation, which have been proved to perform well on natural image compression. Because of the special techniques of radar imaging, SAR images have some distinct properties when compared with natural images that can affect the design of a compression method. First, we introduce SAR properties, sparse representation, and dictionary learning theories. Second, we propose a novel SAR image compression scheme by using multiscale dictionaries. The experimental results carried out on amplitude SAR images reveal that, when compared with JPEG, JPEG2000, and a single-scale dictionary-based compression scheme, the proposed method is better for preserving the important features of SAR images with a competitive compression performance.