Recovering a signal from its amplitude spectrogram, or phase recovery, exhibits many applications in acoustic signal processing. When only an amplitude spectrogram is available and no explicit information is given for the phases, such as often in speech synthesis, the Griffin–Lim algorithm (GLA) is one of the most utilized methods for phase recovery. However, GLA often requires many iterations and results in low perceptual quality in some cases. In this paper, we propose two novel algorithms based on GLA and the alternating direction method of multipliers (ADMM) for better recovery with fewer iteration. ADMM requires extra addition and subtraction related to its auxiliary variable in the time-frequency domain, which effectively modifies phase. Evaluations are performed with both objective measure and subjective test.
The reconstructed signals from an amplitude of clean speech in CMU arctic database [1] by GLA [2], fast GLA (FGLA) [3], and the proposed algorithm [4] are compared.
The example script (in Matlab) for the proposed ADMMGLA is available here.
[1] J. Kominek, and A. W. Black, "The CMU Arctic Speech Databases," in Proc. 5th ISCA Speech Synthesis Workshop (SSW5), June 2004. pp. 223--224.
[2] D. Griffin and J. Lim, "Signal estimation from modified short-time Fourier transform," IEEE Trans. Acoust., Speech, Signal Process., vol. 32, no. 2, pp. 236--243, Apr. 1984.
[3] N. Perraudin, P. Balazs, and P. L. Sondergaard, "A fast Griffin-Lim algorithm," in IEEE Workshop Appl. Signal Process. Audio Acoust., Oct. 2013, pp. 1--4.
[4] Y. Masuyama, K. Yatabe and Y. Oikawa, "Griffin-Lim like phase recovery via alternating direction method of multipliers," IEEE Signal Process. Lett., vol.26, no.1, pp.184--188, Jan. 2019.