We present a dequantization method that employs a phase-aware regularizer, originally successfully applied in an audio inpainting problem. The method promotes a temporal continuity of sinusoidal components in the time-frequency representation of the audio signal, and avoids energy loss artifacts commonly encountered with l1-based regularization approaches. The proposed method is called the Phase-Aware Audio Dequantizer (PHADQ). The method is evaluated against the state-of-the-art using the SDR and PEMO-Q ODG objective metrics, and a subjective MUSHRA-like test.