# A Survey of Deep Learning for Complex Speech Spectrograms

arXiv: https://arxiv.org/abs/2505.08694 · HTML: https://mlsanity.com/paper/2505.08694/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 92 of its 154 references that are in the map.
- First posted on arXiv 13 May 2025.

## Builds on (most cited first, 30 of 92)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Conformer: Convolution-augmented Transformer for Speech Recognition](https://mlsanity.com/paper/2005.08100/) (2020)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [HiFi-GAN: Generative Adversarial Networks for Efficient and High Fidelity Speech Synthesis](https://mlsanity.com/paper/2010.05646/) (2020)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Supervised Speech Separation Based on Deep Learning: An Overview](https://mlsanity.com/paper/1708.07524/) (2017)
- [Deep clustering: Discriminative embeddings for segmentation and separation](https://mlsanity.com/paper/1508.04306/) (2015)
- [Speech Enhancement and Dereverberation with Diffusion-based Generative Models](https://mlsanity.com/paper/2208.05830/) (2022)
- [Permutation Invariant Training of Deep Models for Speaker-Independent Multi-talker Speech Separation](https://mlsanity.com/paper/1607.00325/) (2016)
- [Dual-path RNN: efficient long sequence modeling for time-domain single-channel speech separation](https://mlsanity.com/paper/1910.06379/) (2019)
- [SEGAN: Speech Enhancement Generative Adversarial Network](https://mlsanity.com/paper/1703.09452/) (2017)
- [DCCRN: Deep Complex Convolution Recurrent Network for Phase-Aware Speech Enhancement](https://mlsanity.com/paper/2008.00264/) (2020)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [GANSynth: Adversarial Neural Audio Synthesis](https://mlsanity.com/paper/1902.08710/) (2019)
- [StoRM: A Diffusion-based Stochastic Regeneration Model for Speech Enhancement and Dereverberation](https://mlsanity.com/paper/2212.11851/) (2022)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [Multi-talker Speech Separation with Utterance-level Permutation Invariant Training of Deep Recurrent Neural Networks](https://mlsanity.com/paper/1703.06284/) (2017)
- [Full-Capacity Unitary Recurrent Neural Networks](https://mlsanity.com/paper/1611.00035/) (2016)
- [An Overview of Deep-Learning-Based Audio-Visual Speech Enhancement and Separation](https://mlsanity.com/paper/2008.09586/) (2020)
- [Phase-aware Speech Enhancement with Deep Complex U-Net](https://mlsanity.com/paper/1903.03107/) (2019)

## Built on by (most cited first, 3 of 3)

- [Learning Physiology-Informed Vocal Spectrotemporal Representations for Speech Emotion Recognition](https://mlsanity.com/paper/2602.13259/) (2026)
- [Exploring Resolution-Wise Shared Attention in Hybrid Mamba-U-Nets for Improved Cross-Corpus Speech Enhancement](https://mlsanity.com/paper/2510.01958/) (2025)
- [BinauralVAE: Spatial Audio Reconstruction For World Models](https://mlsanity.com/paper/2609.06837/) (2026)

## Abstract (arXiv)

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.