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The restoration of clipped audio signals, commonly known as declipping, is important to achieve an improved level of audio quality in many audio applications. In this paper, a novel declipping algorithm is presented, jointly based on the theory of compressed sensing (CS) and on well-established properties of human auditory perception. Declipping is formulated as a sparse signal recovery problem using the CS framework. By additionally exploiting knowledge of human auditory perception, a novel perceptual compressed sensing (PCS) framework is devised. A PCS-based declipping algorithm is proposed which uses ℓ1-norm type reconstruction. Comparative objective and subjective evaluation experiments reveal a significant audio quality increase for the proposed PCS-based declipping algorithm compared to CS-based declipping algorithms.