  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.
