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We present a method for estimating the amount of noise and blur in a distorted image. Our method is based on the multiscale structural similarity (MS-SSIM) framework that, although designed to measure image quality, is used to estimate the amount of blur and noise in a degraded image given a reference image. We show that there exists a bijective mapping between the 2-D noise/blur space and the 3-D MS-SSIM space, which allows to recover distortion parameters. That mapping allows to formulate the multidistortion-estimation problem as a classical optimization problem. Various search strategies such as Newton, simplex, NewUOA, and brute-force search are presented and compared. We also show that a bicubic patch can be used to approximate the bijective mapping between the noise/blur space and the 3-D MS-SSIM space. Interestingly, the use of such a patch reduces the processing time by a factor of 40 without significantly reducing precision. Based on quantitative results, we show that the amount of different types of blur and noise in a distorted image can be recovered with accuracy of roughly 2% and 8%, respectively. Our methods are compared with four state-of-the-art noise- and blur-estimation techniques.