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We aim to assess the perceived quality of estimated source signals in the context of audio source separation. These signals may involve one or more kinds of distortions, including distortion of the target source, interference from the other sources or musical noise artifacts. We propose a subjective test protocol to assess the perceived quality with respect to each kind of distortion and collect the scores of 20 subjects over 80 sounds. We then propose a family of objective measures aiming to predict these subjective scores based on the decomposition of the estimation error into several distortion components and on the use of the PEMO-Q perceptual salience measure to provide multiple features that are then combined. These measures increase correlation with subjective scores up to 0.5 compared to nonlinear mapping of individual state-of-the-art source separation measures. Finally, we released the data and code presented in this paper in a freely available toolkit called PEASS.