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While noise is usually regarded as a problem of the image formation process, we observe that it is also frequently part of natural texture. In this paper, we present a concept for improved compression of noisy texture in natural images. Since noise is problematic to decorrelation-based compression methods, we propose to perform image decomposition by denoising, followed by separate compression of the components. The denoised component is encoded using conventional methods, while the texture component is compressed by encoding parameters of a texture model. It turns out that at similar bit rates, our method can improve visual quality.