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We propose an optimization-based method for reconstructing a time-domainsignal from a low-dimensional spectral representation such as amel-spectrogram. Phase reconstruction has been studied to reconstruct atime-domain signal from the full-band short-time Fourier transform (STFT)magnitude. The Griffin-Lim algorithm (GLA) has been widely used because itrelies only on the redundancy of STFT and is applicable to various audiosignals. In this paper, we jointly reconstruct the full-band magnitude andphase by considering the bi-level relationships among the time-domain signal,its STFT coefficients, and its mel-spectrogram. The proposed method isformulated as a rigorous optimization problem and estimates the full-bandmagnitude based on the criterion used in GLA. Our experiments demonstrate theeffectiveness of the proposed method on speech, music, and environmentalsignals.

Signal Reconstruction from Mel-spectrogram Based on Bi-level Consistency of Full-band Magnitude and Phase