Recent advancements in deep learning have significantly impacted the field of speech signal processing, particularly in the analysis and manipulation of complex spectrograms. This survey provides a comprehensive overview of the state-of-the-art techniques leveraging deep neural networks for processing complex spectrograms, which encapsulate both magnitude and phase information. We begin by introducing complex spectrograms and their associated features for various speech processing tasks. Next, we examine the key components and architectures of complex-valued neural networks, which are specifically designed to handle complex-valued data and have been applied to complex spectrogram processing. As recent studies have primarily focused on applying real-valued neural networks to complex spectrograms, we revisit these approaches and their architectural designs. We then discuss various training strategies and loss functions tailored for training neural networks to process and model complex spectrograms. The survey further examines key applications, including phase retrieval, speech enhancement, and speaker separation, where deep learning has achieved significant progress by leveraging complex spectrograms or their derived feature representations. Additionally, we examine the intersection of complex spectrograms with generative models. This survey aims to serve as a valuable resource for researchers and practitioners in the field of speech signal processing, deep learning and related fields.

Recent advancements in generative modeling have significantly enhanced the reconstruction of audio waveforms from various representations. While diffusion models are adept at this task, they are hindered by latency issues due to their operation at the individual sample point level and the need for numerous sampling steps. In this study, we introduce RFWave, a cutting-edge multi-band Rectified Flow approach designed to reconstruct high-fidelity audio waveforms from Mel-spectrograms or discrete tokens. RFWave uniquely generates complex spectrograms and operates at the frame level, processing all subbands simultaneously to boost efficiency. Leveraging Rectified Flow, which targets a flat transport trajectory, RFWave achieves reconstruction with just 10 sampling steps. Our empirical evaluations show that RFWave not only provides outstanding reconstruction quality but also offers vastly superior computational efficiency, enabling audio generation at speeds up to 97 times faster than real-time on a GPU.

Diffusion probabilistic models have been recently used in a variety of Diffusion-based generative models are a recent innovation that tasks, including speech enhancement and synthesis. As a generative has already been shown to be very effective on various computer approach, diffusion models have been shown to be especially suitable vision tasks, including inpainting [11], super-resolution [12], text-toimage for imputation problems, where missing data is generated based on mapping [13] and more [14]. Their application is, however, not existing data. Phase retrieval is inherently an imputation problem, limited to vision tasks and they have already been used in other fields, where phase information has to be generated based on the given including text-to-speech [15], as well as speech enhancement and magnitude. In this work we build upon previous work in the speech dereverberation [16]-[19]. The basic idea is gradual addition of noise domain, adapting a speech enhancement diffusion model specifically to a clean sample until a completely corrupted sample is obtained.

Diffusion-based speech enhancement (SE) has been investigated recently, but its decoding is very time-consuming. One solution is to initialize the decoding process with the enhanced feature estimated by a predictive SE system. However, this two-stage method ignores the complementarity between predictive and diffusion SE. In this paper, we propose a unified system that integrates these two SE modules. The system encodes both generative and predictive information, and then applies both generative and predictive decoders, whose outputs are fused. Specifically, the two SE modules are fused in the first and final diffusion steps: the first step fusion initializes the diffusion process with the predictive SE for improving the convergence, and the final step fusion combines the two complementary SE outputs to improve the SE performance. Experiments on the Voice-Bank dataset show that the diffusion score estimation can benefit from the predictive information and speed up the decoding.

Speech enhancement models have greatly progressed in recent years, but still show limits in perceptual quality of their speech outputs. We propose an objective for perceptual quality based on temporal acoustic parameters. These are fundamental speech features that play an essential role in various applications, including speaker recognition and paralinguistic analysis. We provide a differentiable estimator for four categories of low-level acoustic descriptors involving: frequency-related parameters, energy or amplitude-related parameters, spectral balance parameters, and temporal features. Unlike prior work that looks at aggregated acoustic parameters or a few categories of acoustic parameters, our temporal acoustic parameter (TAP) loss enables auxiliary optimization and improvement of many fine-grain speech characteristics in enhancement workflows. We show that adding TAPLoss as an auxiliary objective in speech enhancement produces speech with improved perceptual quality and intelligibility. We use data from the Deep Noise Suppression 2020 Challenge to demonstrate that both time-domain models and time-frequency domain models can benefit from our method.

Several speech processing systems have demonstrated considerable performance improvements when deep complex neural networks (DCNN) are coupled with self-attention (SA) networks. However, the majority of DCNN-based studies on speech dereverberation that employ self-attention do not explicitly account for the inter-dependencies between real and imaginary features when computing attention. In this study, we propose a complex-valued T-F attention (TFA) module that models spectral and temporal dependencies by computing two-dimensional attention maps across time and frequency dimensions. We validate the effectiveness of our proposed complex-valued TFA module with the deep complex convolutional recurrent network (DCCRN) using the REVERB challenge corpus. Experimental findings indicate that integrating our complex-TFA module with DCCRN improves overall speech quality and performance of back-end speech applications, such as automatic speech recognition, compared to earlier approaches for self-attention.

Binaural rendering of ambisonic signals is of broad interest to virtual reality and immersive media. Conventional methods often require manually measured Head-Related Transfer Functions (HRTFs). To address this issue, we collect a paired ambisonic-binaural dataset and propose a deep learning framework in an end-to-end manner. Experimental results show that neural networks outperform the conventional method in objective metrics and achieve comparable subjective metrics. To validate the proposed framework, we experimentally explore different settings of the input features, model structures, output features, and loss functions. Our proposed system achieves an SDR of 7.32 and MOSs of 3.83, 3.58, 3.87, 3.58 in quality, timbre, localization, and immersion dimensions.

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.