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In this paper, we propose a new general Quality Assessment method based on the curvelet transform, called Curvelet No-Reference (CNR) model, which can estimate levels of noise, blur and JPEG 2000 compression of natural images. The peak coordinate of the curvelet coefficient histogram occupies distinctive regions depending on how the image was modified from the original. During training, we associate peak positions with known filter levels. In the prediction stage, the filter levels of new images are estimated from the training data, with no access to the reference images. We tested CNR both on our own image dataset and on LIVE. Results demonstrate that CNR does a better job at predicting noise and blur levels among several methods, including SSIM and PSNR. We also present an accelerated version of CNR that does not sacrifice prediction accuracy on natural images.