This paper presents a novel phase reconstruction method (only from a given amplitude spectrogram) by combining a signal-processing-based approach and a deep neural network (DNN). To retrieve a time-domain signal from its amplitude spectrogram, the corresponding phase is required. One of the popular phase reconstruction methods is the Griffin-Lim algorithm (GLA), which is based on the redundancy of the short-time Fourier transform. However, GLA often involves many iterations and produces low-quality signals owing to the lack of prior knowledge of the target signal. In order to address these issues, in this study, we propose an architecture which stacks a sub-block including two GLA-inspired fixed layers and a DNN. The number of stacked sub-blocks is adjustable, and we can trade the performance and computational load based on requirements of applications. The effectiveness of the proposed method is investigated by reconstructing phases from amplitude spectrograms of speeches.
Recently, DNNs including fixed STFT (and iSTFT) layers were considered for treating phase information within the networks. A generative adversarial network (GAN)-based approach to reconstruct a complex-valued spectrogram solely from a given amplitude spectrogram was presented in @cite_22 . The output of the generator (a complex-valued spectrogram) is converted back to the time domain by iSTFT layer and inputted to the discriminator, where this iSTFT layer is essential for its training as discussed in @cite_22 . As another example, a DNN for speech separation @cite_3 employed the multiple input spectrogram inverse (MISI) layer which consists of the pair of STFT and iSTFT as in GLA. The MISI layer is applied to the output of the DNN for speech separation to improve its performance by considering the effect of the phase reconstruction together with the separation. In addition, in @cite_36 , the time-frequency representation was also trained with the DNN for speech separation. The success of these DNNs indicates that considering STFT (and iSTFT) together with a DNN is important for treating phase.
@cite_36 @cite_22 @cite_3
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Progress in solving the cocktail party problem, i.e., separating the speech from multiple overlapping speakers, has recently accelerated with the invention of techniques such as deep clustering and permutation free mask inference. These approaches typically focus on estimating target STFT magnitudes and ignore problems of phase inconsistency. In this paper, we explicitly integrate phase reconstruction into our separation algorithm using a loss function defined on time-domain signals. A deep neural network structure is defined by unfolding a phase reconstruction algorithm and treating each iteration as a layer in our network. Furthermore, instead of using fixed STFT iSTFT time-frequency representations, we allow our network to learn a modified version of these representations from data. We compare several variants of these unfolded phase reconstruction networks achieving state of the art results on the publicly available wsj0-2mix dataset, and show improved performance when the STFT iSTFT-like representations are allowed to adapt. In this paper, we address the problem of reconstructing a time-domain signal (or a phase spectrogram) solely from a magnitude spectrogram. Since magnitude spectrograms do not contain phase information, we must restore or infer phase information to reconstruct a time-domain signal. One widely used approach for dealing with the signal reconstruction problem was proposed by Griffin and Lim. This method usually requires many iterations for the signal reconstruction process and depending on the inputs, it does not always produce high-quality audio signals. To overcome these shortcomings, we apply a learning-based approach to the signal reconstruction problem by modeling the signal reconstruction process using a deep neural network and training it using the idea of a generative adversarial network. Experimental evaluations revealed that our method was able to reconstruct signals faster with higher quality than the Griffin-Lim method. This paper proposes an end-to-end approach for single-channel speaker-independent multi-speaker speech separation, where time-frequency (T-F) masking, the short-time Fourier transform (STFT), and its inverse are represented as layers within a deep network. Previous approaches, rather than computing a loss on the reconstructed signal, used a surrogate loss based on the target STFT magnitudes. This ignores reconstruction error introduced by phase inconsistency. In our approach, the loss function is directly defined on the reconstructed signals, which are optimized for best separation. In addition, we train through unfolded iterations of a phase reconstruction algorithm, represented as a series of STFT and inverse STFT layers. While mask values are typically limited to lie between zero and one for approaches using the mixture phase for reconstruction, this limitation is less relevant if the estimated magnitudes are to be used together with phase reconstruction. We thus propose several novel activation functions for the output layer of the T-F masking, to allow mask values beyond one. On the publicly-available wsj0-2mix dataset, our approach achieves state-of-the-art 12.6 dB scale-invariant signal-to-distortion ratio (SI-SDR) and 13.1 dB SDR, revealing new possibilities for deep learning based phase reconstruction and representing a fundamental progress towards solving the notoriously-hard cocktail party problem.