Hartley Spectral Pooling for Deep Learning

Abstract

In most convolution neural networks (CNNs), downsampling hidden layers is adopted for increasing computation efficiency and the receptive field size. Such operation is commonly called pooling. Maximization 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 spectral pooling proposed by Rippel et al. [1], we present the Hartley transform based spectral pooling method. The proposed spectral pooling avoids the use of complex arithmetic for frequency representation, in comparison with Fourier pooling. The new approach preserves more structure features for network's discriminability than max and average pooling. We empirically show the Hartley pooling gives rise to the convergence of training CNNs on MNIST and CIFAR-10 datasets.

LEACS: a learnable and efficient active contour model with space-frequency pooling for medical image segmentation

“…It allows pooling to any desired output dimensionality while retaining significantly more spatial structure-related information than other pooling approaches with the same number of parameters. We propose a spacefrequency pooling method that combines max pooling and spectral pooling (Zhang and Ma 2018) to improve the boundary location performance of small scale complex medical image datasets.…”