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The satisfied user ratio (SUR) curve for a lossy image compression scheme, e.g., JPEG, characterizes the complementary cumulative distribution function of the just noticeable difference (JND), the smallest distortion level that can be perceived by a subject when a reference image is compared to a distorted one. A sequence of JNDs can be defined with a suitable successive choice of reference images. We propose the first deep learning approach to predict SUR curves. We show how to apply maximum likelihood estimation and the Anderson-Darling test to select a suitable parametric model for the distribution function. We then use deep feature learning to predict samples of the SUR curve and apply the method of least squares to fit the parametric model to the predicted samples. Our deep learning approach relies on a siamese convolutional neural network, transfer learning, and deep feature learning, using pairs consisting of a reference image and a compressed image for training. Experiments on the MCL-JCI dataset showed state-of-the-art performance. For example, the mean Bhattacharyya distances between the predicted and ground truth first, second, and third JND distributions were 0.0810, 0.0702, and 0.0522, respectively, and the corresponding average absolute differences of the peak signal-to-noise ratio at a median of the first JND distribution were 0.58, 0.69, and 0.58 dB. Further experiments on the JND-Pano dataset showed that the method transfers well to high resolution panoramic images viewed on head-mounted displays.