Deep Griffin–Lim Iteration: Trainable Iterative Phase Reconstruction Using Neural Network

In this paper, we propose a phase reconstruction framework, named Deep Griffin-Lim Iteration (DeGLI). Phase reconstruction is a fundamental technique for improving the quality of sound obtained through some process in the time-frequency domain. It has been shown that the recent methods using deep neural networks (DNN) outperformed the conventional iterative phase reconstruction methods such as the Griffin-Lim algorithm (GLA). However, the computational cost of DNN-based methods is not adjustable at the time of inference, which may limit the range of applications. To address this problem, we combine the iterative structure of GLA with a DNN so that the computational cost becomes adjustable by changing the number of iterations of the proposed DNN-based component. A training method that is independent of the number of iterations for inference is also proposed to minimize the computational cost of the training. This training method, named sub-block training by denoising (SBTD), avoids recursive use of the DNN and enables training of DeGLI with a single sub-block (corresponding to one GLA iteration). Furthermore, we propose a complex DNN based on complex convolution layers with gated mechanisms and investigated its performance in terms of the proposed framework. Through several experiments, we found that DeGLI significantly improved both objective and subjective measures from GLA by incorporating the DNN, and its sound quality was comparable to those of neural vocoders.