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A compression quality prediction model is proposed for grey images coding with JPEG2000. With this model, the compression quality (PSNR) could be estimated according to the given compression ratio (CR) and the image activity measures (IAM) without coding images. The image activity measure is the weighted sum of the IAM values based on the 1-pixel-distance and 2-pixel-distance gradients along horizontal and vertical directions. We have shown that IAM is a function of the image variance and autocorrelation coefficients. Based on Shannon's rate-distortion theorem, a theoretical justification is provided for the correlation of IAM with PSNR. Experimental results show that the prediction error is lower than 1 dB for more than 70% sample images when CR is higher than 15. The prediction error is less than 2 dB for over 90% images. This prediction performance is acceptable for general applications.