Non-Griffin–Lim Type Signal Recovery from Magnitude Spectrogram

Speech and audio signal processing frequently requires to recover a time-domain signal from the magnitude of a spectrogram. Conventional methods inversely transform the magnitude spectrogram with a phase spectrogram recovered by the Griffin–Lim algorithm or its accelerated versions. The short-time Fourier transform (STFT) perfectly matches this framework, while other useful spectrogram transforms, such as the constant-Q transform (CQT), do not, because their inverses cannot be computed easily. To make the best of such useful spectrogram transforms, we propose an algorithm which recovers the time-domain signal without the inverse spectrogram transforms. We formulate the signal recovery as a nonconvex optimization problem, which is difficult to solve exactly. To approximately solve the problem, we exploit a stochastic convex optimization technique. A well-organized block selection enables us both to avoid local minimums and to achieve fast convergence. Numerical experiments show the effectiveness of the proposed method for both STFT and CQT cases.