Two-stage phase reconstruction using DNN and von Mises distribution-based maximum likelihood

This paper presents an improvement to a two-stage algorithm for estimating the phase from only the amplitude with deep neural networks (DNNs). Rather than directly estimating the phase, the two-stage method estimates phase derivatives, i.e., instantaneous frequency (IF) and group delay (GD), by using DNNs in the first stage, and it then reconstructs the phase from those derivatives using a least-squares (LS) method in the second stage. A problem with the algorithm is that the periodicity of the estimated IF and GD significantly affects the results of LS estimation. In this paper, we replace the LS method in the second stage with a new maximum-likelihood method using von Mises distribution. The error function is minimized by using a regularized Newton's method. Experimental results demonstrate that the proposed method can reduce the IF and GD errors of the reconstructed phase in the second stage and achieve a higher overall speech quality than conventional methods.