This paper presents improvements to real-time phase reconstruction using deep neural networks (DNNs).The advantage of DNN-based approaches in phase reconstruction is that they can leverage prior knowledge from data and are adaptable to realtime applications by using causal models.However, conventional DNN-based methods do not consider the varying properties of the phase at different time-frequency bins.Our paper proposes loss functions for phase reconstruction that incorporate frequency-specific and amplitude weights to distinguish the importance of phase elements based on their properties.We also use an extension of the group delay to improve the phase connections along the frequency.To improve the generalization, we augment the data by randomly shifting the signals in the time domain for each epoch during training.Experimental results show the superior performance of the proposed methods compared to conventional DNN-based and non-DNN real-time phase reconstruction methods.

This paper presents improvements to two-stage algorithms for estimating the short-time Fourier transform (STFT) phase from only the amplitude by using deep neural networks (DNNs). The phase is difficult to reconstruct due to its sensitivity to the waveform shift and wrapping issue. To mitigate these problems, two-stage approaches indirectly estimate the phase through phase derivatives, i.e., instantaneous frequency (IF) and group delay (GD). In the first stage, the IF and GD are estimated from the amplitude using DNNs, and then in the second stage, the phase is reconstructed by maintaining the IF/GD information. Conventional methods for the second stage do not consider the importance of high-amplitude time–frequency bins, e.g., the least squares-based method, or lack a solid model, e.g., the average-based method. To address these problems, we propose improvements to the second stage of two-stage algorithms by usingvon Misesdistribution-based maximum likelihood and weighted least squares. We also provide theoretical discussions for the phase reconstruction, including the investigations of the properties of the GD and roles of the IF/GD information in the inverse STFT. On the basis of the analysis, we propose a new phase-based feature, i.e., inter-frequency phase difference (IFPD), and demonstrate its application in two-stage phase reconstruction algorithms. We conducted subjective and objective experiments to compare the performances of our proposed and conventional methods. The results confirm that the proposed method using the IFPD performs better than other methods for all metrics.