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Wavelet image decomposition generates a hierarchical data structure to represent an image. Recently, a new class of image compression algorithms has been developed for exploiting dependencies between the hierarchical wavelet coefficients using zerotrees. This paper deals with a fuzzy inference filter for image entropy coding by choosing significant coefficients and zerotree roots in the higher frequency wavelet subbands. Moreover, an adaptive quantization is proposed to improve the coding performance. Evaluating with the standard images, the proposed approaches are comparable or superior to most state-of-the-art coders. Based on the fuzzy energy judgment, the proposed approaches can achieve an excellent performance on the combination applications of image compression and watermarking.