  In most convolution neural networks (CNNs), downsampling hidden layers is
adopted for increasing computation efficiency and the receptive field size.
Such operation is commonly so-called pooling. Maximation and averaging over
sliding windows (max/average pooling), and plain downsampling in the form of
strided convolution are popular pooling methods. Since the pooling is a lossy
procedure, a motivation of our work is to design a new pooling approach for
less lossy in the dimensionality reduction. Inspired by the Fourier spectral
pooling(FSP) proposed by Rippel et. al. [1], we present the Hartley transform
based spectral pooling method in CNNs. Compared with FSP, the proposed spectral
pooling avoids the use of complex arithmetic for frequency representation and
reduces the computation. Spectral pooling preserves more structure features for
network's discriminability than max and average pooling. We empirically show
that Hartley spectral pooling gives rise to the convergence of training CNNs on
MNIST and CIFAR-10 datasets.

Computer Vision and Pattern Recognition;Machine Learning;Signal Processing;Machine Learning