# Dual Quaternion Ambisonics Array for Six-Degree-of-Freedom Acoustic Representation

arXiv: https://arxiv.org/abs/2204.01851 · HTML: https://mlsanity.com/paper/2204.01851/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 53 references that are in the map.
- First posted on arXiv 4 Apr 2022.

## Builds on (most cited first, 19 of 19)

- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [FSD50K: An Open Dataset of Human-Labeled Sound Events](https://mlsanity.com/paper/2010.00475/) (2020)
- [Sound Event Localization and Detection of Overlapping Sources Using Convolutional Recurrent Neural Networks](https://mlsanity.com/paper/1807.00129/) (2018)
- [An Overview of Deep-Learning-Based Audio-Visual Speech Enhancement and Separation](https://mlsanity.com/paper/2008.09586/) (2020)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [A Wavenet for Speech Denoising](https://mlsanity.com/paper/1706.07162/) (2017)
- [Move2Hear: Active Audio-Visual Source Separation](https://mlsanity.com/paper/2105.07142/) (2021)
- [Overview and Evaluation of Sound Event Localization and Detection in DCASE 2019](https://mlsanity.com/paper/2009.02792/) (2020)
- [PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions](https://mlsanity.com/paper/2110.04176/) (2021)
- [Quaternion Generative Adversarial Networks](https://mlsanity.com/paper/2104.09630/) (2021)
- [Node Co-occurrence based Graph Neural Networks for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2104.07396/) (2021)
- [A Quaternion-Valued Variational Autoencoder](https://mlsanity.com/paper/2010.11647/) (2020)
- [L3DAS22 Challenge: Learning 3D Audio Sources in a Real Office Environment](https://mlsanity.com/paper/2202.10372/) (2022)
- [L3DAS21 Challenge: Machine Learning for 3D Audio Signal Processing](https://mlsanity.com/paper/2104.05499/) (2021)
- [SELD-TCN: Sound Event Localization & Detection via Temporal Convolutional Networks](https://mlsanity.com/paper/2003.01609/) (2020)
- [Predicting Rigid Body Dynamics using Dual Quaternion Recurrent Neural Networks with Quaternion Attention](https://mlsanity.com/paper/2011.08734/) (2020)
- [Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modelling](https://mlsanity.com/paper/2104.01716/) (2021)
- [SALADnet: Self-Attentive multisource Localization in the Ambisonics Domain](https://mlsanity.com/paper/2107.11066/) (2021)
- [Direction of Arrival Estimation of Noisy Speech Using Convolutional Recurrent Neural Networks with Higher-Order Ambisonics Signals](https://mlsanity.com/paper/2102.09853/) (2021)

## Built on by (most cited first, 8 of 8)

- [Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2401.02277/) (2024)
- [Learning Speech Emotion Representations in the Quaternion Domain](https://mlsanity.com/paper/2204.02385/) (2022)
- [Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2209.02456/) (2022)
- [Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2309.07716/) (2023)
- [Towards Explaining Hypercomplex Neural Networks](https://mlsanity.com/paper/2403.17929/) (2024)
- [PHYDI: Initializing Parameterized Hypercomplex Neural Networks as Identity Functions](https://mlsanity.com/paper/2310.07612/) (2023)
- [PHemoNet: A Multimodal Network for Physiological Signals](https://mlsanity.com/paper/2410.00010/) (2024)
- [Demystifying the Hypercomplex: Inductive Biases in Hypercomplex Deep Learning](https://mlsanity.com/paper/2405.07024/) (2024)

## Abstract (arXiv)

Spatial audio methods are gaining a growing interest due to the spread of immersive audio experiences and applications, such as virtual and augmented reality. For these purposes, 3D audio signals are often acquired through arrays of Ambisonics microphones, each comprising four capsules that decompose the sound field in spherical harmonics. In this paper, we propose a dual quaternion representation of the spatial sound field acquired through an array of two First Order Ambisonics (FOA) microphones. The audio signals are encapsulated in a dual quaternion that leverages quaternion algebra properties to exploit correlations among them. This augmented representation with 6 degrees of freedom (6DOF) involves a more accurate coverage of the sound field, resulting in a more precise sound localization and a more immersive audio experience. We evaluate our approach on a sound event localization and detection (SELD) benchmark. We show that our dual quaternion SELD model with temporal convolution blocks (DualQSELD-TCN) achieves better results with respect to real and quaternion-valued baselines thanks to our augmented representation of the sound field. Full code is available at: https://github.com/ispamm/DualQSELD-TCN.