Mel-Spectrogram Inversion via Alternating Direction Method of Multipliers

Signal reconstruction from its mel-spectrogram is known as mel-spectrogram inversion and has many applications, including speech and foley sound synthesis. In this paper, we propose a mel-spectrogram inversion method based on a rigorous optimization algorithm. To reconstruct a time-domain signal with inverse short-time Fourier transform (STFT), both full-band STFT magnitude and phase should be predicted from a given mel-spectrogram. Their joint estimation has outperformed the cascaded full-band magnitude prediction and phase reconstruction by preventing error accumulation. However, the existing joint estimation method requires many iterations, and there remains room for performance improvement. We present an alternating direction method of multipliers (ADMM)-based joint estimation method motivated by its success in various nonconvex optimization problems including phase reconstruction. An efficient update of each variable is derived by exploiting the conditional independence among the variables. Our experiments demonstrate the effectiveness of the proposed method on speech and foley sounds.