Just noticeable difference (JND) models are widely used for perceptual redundancy estimation in images and videos. A common method for measuring the accuracy of a JND model is to inject random noise in an image based on the JND model, and check whether the JND-noise-contaminated image is perceptually distinguishable from the original image or not. Also, when comparing the accuracy of two different JND models, the model that produces the JND-noise-contaminated image with better quality at the same level of noise energy is the better model. But in both of these cases, a subjective test is necessary, which is very time consuming and costly. In this paper, we present a full-reference metric called PDP (perceptual distinguishability predictor), which can be used to determine whether a given JND-noise-contaminated image is perceptually distinguishable from the reference image. The proposed metric employs the concept of sparse coding, and extracts a feature vector out of a given image pair. The feature vector is then fed to a multilayer neural network for classification. To train the network, we built a public database of 999 natural images with distinguishbility thresholds for four different JND models obtained from an extensive subjective experiment. The results indicated that PDD achieves high classification accuracy of 97.1%. The proposed method can be used to objectively compare various JND models without performing any subjective test. It can also be used to obtain proper scaling factors to improve the JND thresholds estimated by an arbitrary JND model.