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

Abstract

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 timefrequency 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 DNNbased 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.

Phase Retrieval With Bregman Divergences and Application to Audio Signal Recovery

“…PR has also been tackled using signal modeling [11], [30], [31] or deep neural networks [32]. However, optimization-based approaches remain efficient, provide theoretical guarantees and may still be used with model-based approaches [33], [34].…”

Beyond Griffin-Lim: Improved Iterative Phase Retrieval for Speech

“…However, it is often set to values close to 1, chosen experimentally as its optimal value strongly depends on signal characteristics. Note that changing the sign of β has the effect of interchanging the projections in ( 11)- (13). For β = 1, the RAAR iteration and DM iteration are identical (this case is also equivalent to several other phase retrieval algorithms [21]).…”

“…Interestingly, GLA was later rediscovered in ptychography as the Error Reduction algorithm [5], [8]. Several extensions of GLA have been proposed over the years, including an accelerated version [9], online variants [10], [11] an adaptation to the source separation context [12] and even augmentation by a neural network [13], but the basic algorithm is still widely used (other approaches not based on iterative projection exist [1] but are outside the scope of this paper). In this work we examine how modern methods from optics perform when applied to speech signals.…”

A Simultaneous Denoising and Dereverberation Framework with Target Decoupling

“…Afterward, the phase information can be effectively modified based on previous results by introducing a global residual connection. The rationale is that there exists implicit relation between magnitude and phase and superb magnitude estimation can profit better recovery for phase [12,19].…”