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Total variation regularization can be used to decompose any natural image into a structure image (edges and smooth areas) and a texture image (texture only). Although structure images can be highly compressed by conventional JPEG methods, texture images require a lot of bits to represent their feature details. Texture images are composed from several repeated patterns, each of which can be synthesized from small texture patches, and we propose a novel image compression method for these images. First, we extract several texture patches from an original texture image. Next, we compress the texture distribution map to a small number of representative points corresponding with each texture patch. The texture image is then synthesized from the texture distribution map and texture patches at the decoder. Experimental results show that the decoded image obtained by our proposed method is subjectively similar to the original one compared with the decoded image by the conventional JPEG.