Neural networks, especially convolutional neural networks (CNN), are one of the most common tools these days used in computer vision. Most of these networks work with real-valued data using real-valued features. Complex-valued convolutional neural networks (CV-CNN) can preserve the algebraic structure of complex-valued input data and have the potential to learn more complex relationships between the input and the ground-truth. Although some comparisons of CNNs and CV-CNNs for different tasks have been performed in the past, a large-scale investigation comparing different models operating on different tasks has not been conducted. Furthermore, because complex features contain both real and imaginary components, CV-CNNs have double the number of trainable parameters as real-valued CNNs in terms of the actual number of trainable parameters. Whether or not the improvements in performance with CV-CNN observed in the past have been because of the complex features or just because of having double the number of trainable parameters has not yet been explored. This paper presents a comparative study of CNN, CNNx2 (CNN with double the number of trainable parameters as the CNN), and CV-CNN. The experiments were performed using seven models for two different tasks - brain tumour classification and segmentation in brain MRIs. The results have revealed that the CV-CNN models outperformed the CNN and CNNx2 models.

翻译：神经网络，尤其是卷积神经网络(CNN)，是当今计算机视觉领域最常用的工具之一。这些网络大多基于实数域特征处理实数数据。复数域卷积神经网络(CV-CNN)能够保留复数输入数据的代数结构，并具备学习输入与真实值之间更复杂关系的潜力。尽管已有研究对CNN和CV-CNN在不同任务中的表现进行了比较，但尚未开展针对不同模型在不同任务上运行的大规模系统性研究。此外，由于复数特征包含实部和虚部，CV-CNN的实际可训练参数数量是实数域CNN的两倍。过去观察到的CV-CNN性能提升究竟源于复数特征本身，还是仅仅因为参数数量翻倍，这一问题尚未得到深入探究。本文对CNN、CNNx2(参数数量为CNN两倍的CNN)和CV-CNN进行了比较研究。实验采用七种模型，针对脑部MRI图像中的脑肿瘤分类与分割两项不同任务展开。结果表明，CV-CNN模型在性能上优于CNN和CNNx2模型。