# Quaternion Convolutional Neural Networks for Heterogeneous Image Processing

arXiv: https://arxiv.org/abs/1811.02656 · HTML: https://mlsanity.com/paper/1811.02656/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2018.

## Built on by (most cited first, 29 of 29)

- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with 1/n Parameters](https://mlsanity.com/paper/2102.08597/) (2021)
- [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)
- [QuatDE: Dynamic Quaternion Embedding for Knowledge Graph Completion](https://mlsanity.com/paper/2105.09002/) (2021)
- [Quaternion-valued Correlation Learning for Few-Shot Semantic Segmentation](https://mlsanity.com/paper/2305.07283/) (2023)
- [Convolutional Filtering and Neural Networks with Non Commutative Algebras](https://mlsanity.com/paper/2108.09923/) (2021)
- [Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss](https://mlsanity.com/paper/2202.02063/) (2022)
- [Hypercomplex Multimodal Emotion Recognition from EEG and Peripheral Physiological Signals](https://mlsanity.com/paper/2310.07648/) (2023)
- [Parameterized Hypercomplex Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/2103.16584/) (2021)
- [Multi-View Hypercomplex Learning for Breast Cancer Screening](https://mlsanity.com/paper/2204.05798/) (2022)
- [Attention-Map Augmentation for Hypercomplex Breast Cancer Classification](https://mlsanity.com/paper/2310.07633/) (2023)
- [Generalizing Medical Image Representations via Quaternion Wavelet Networks](https://mlsanity.com/paper/2310.10224/) (2023)
- [Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modelling](https://mlsanity.com/paper/2104.01716/) (2021)
- [Hypercomplex Image-to-Image Translation](https://mlsanity.com/paper/2205.02087/) (2022)
- [RingCNN: Exploiting Algebraically-Sparse Ring Tensors for Energy-Efficient CNN-Based Computational Imaging](https://mlsanity.com/paper/2104.09056/) (2021)
- [QSAM-Net: Rain streak removal by quaternion neural network with self-attention module](https://mlsanity.com/paper/2208.04346/) (2022)
- [Quaternion Convolutional Neural Networks: Current Advances and Future Directions](https://mlsanity.com/paper/2307.08663/) (2023)
- [Time Series Compression using Quaternion Valued Neural Networks and Quaternion Backpropagation](https://mlsanity.com/paper/2403.11722/) (2024)
- [PHemoNet: A Multimodal Network for Physiological Signals](https://mlsanity.com/paper/2410.00010/) (2024)
- [Quaternion-Valued Convolutional Neural Network Applied for Acute Lymphoblastic Leukemia Diagnosis](https://mlsanity.com/paper/2112.06685/) (2021)
- [Quaternion recurrent neural network with real-time recurrent learning and maximum correntropy criterion](https://mlsanity.com/paper/2402.14227/) (2024)
- [Improving Quaternion Neural Networks with Quaternionic Activation Functions](https://mlsanity.com/paper/2406.16481/) (2024)
- [HyReaL: Clustering Attributed Graph via Hyper-Complex Space Representation Learning](https://mlsanity.com/paper/2411.14727/) (2024)
- [Deep Axial Hypercomplex Networks](https://mlsanity.com/paper/2301.04626/) (2023)
- [Non Commutative Convolutional Signal Models in Neural Networks: Stability to Small Deformations](https://mlsanity.com/paper/2310.03879/) (2023)
- [KHNNs: hypercomplex neural networks computations via Keras using TensorFlow and PyTorch](https://mlsanity.com/paper/2407.00452/) (2024)
- [CMAWRNet: Multiple Adverse Weather Removal via a Unified Quaternion Neural Architecture](https://mlsanity.com/paper/2505.01882/) (2025)
- [Cross-Fitted Residual Utility for Primary-Preserving Cognitive Decision Correction in Automatic Modulation Classification](https://mlsanity.com/paper/2608.02063/) (2026)

## Abstract (arXiv)

Convolutional neural networks (CNN) have recently achieved state-of-the-art results in various applications. In the case of image recognition, an ideal model has to learn independently of the training data, both local dependencies between the three components (R,G,B) of a pixel, and the global relations describing edges or shapes, making it efficient with small or heterogeneous datasets. Quaternion-valued convolutional neural networks (QCNN) solved this problematic by introducing multidimensional algebra to CNN. This paper proposes to explore the fundamental reason of the success of QCNN over CNN, by investigating the impact of the Hamilton product on a color image reconstruction task performed from a gray-scale only training. By learning independently both internal and external relations and with less parameters than real valued convolutional encoder-decoder (CAE), quaternion convolutional encoder-decoders (QCAE) perfectly reconstructed unseen color images while CAE produced worst and gray-scale versions.