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A quality constrained compression algorithm based on discrete wavelet transform (DWT) is proposed. The spatial-frequency decomposition property of DWT provides possibility for not only the new compression algorithm but also a frequency-domain quality assessment method. For facilitating the new algorithm, a new quality metric in the wavelet domain called WNMSE is suggested, which assesses the quality of an image with the weighted sum of normalized mean square errors of the wavelet coefficients. The metric is consistent with the human judgment of visual quality as well as able to estimate the quality during the compression process. Based on the relationship between the statistic features, quantization steps, and the weighted normalized mean square error value of the image, we develop a quality constrained quantization algorithm which can determine the quantization step-sizes for all the wavelet subbands for compressing the image to a desired visual quality accurately.