Pooling and unpooling are two essential operations in constructing
hierarchical spherical convolutional neural networks (HS-CNNs) for
comprehensive feature learning in the spherical domain. Most existing models
employ downsampling-based pooling, which will inevitably incur information loss
and cannot adapt to different spherical signals and tasks. Besides, the
preserved information after pooling cannot be well restored by the subsequent
unpooling to characterize the desirable features for a task. In this paper, we
propose a novel framework of HS-CNNs with a lifting structure to learn adaptive
spherical wavelets for pooling and unpooling, dubbed LiftHS-CNN, which ensures
a more efficient hierarchical feature learning for both image- and pixel-level
tasks. Specifically, adaptive spherical wavelets are learned with a lifting
structure that consists of trainable lifting operators (i.e., update and
predict operators). With this learnable lifting structure, we can adaptively
partition a signal into two sub-bands containing low- and high-frequency
components, respectively, and thus generate a better down-scaled representation
for pooling by preserving more information in the low-frequency sub-band. The
update and predict operators are parameterized with graph-based attention to
jointly consider the signal's characteristics and the underlying geometries. We
further show that particular properties are promised by the learned wavelets,
ensuring the spatial-frequency localization for better exploiting the signal's
correlation in both spatial and frequency domains. We then propose an unpooling
operation that is invertible to the lifting-based pooling, where an inverse
wavelet transform is performed by using the learned lifting operators to
restore an up-scaled representation. Extensive empirical evaluations on various
spherical domain tasks validate the superiority of the proposed LiftHS-CNN.

本文提出了一种新的 HS-CNN 框架，名为 LiftHS-CNN，其采用可学习的 lifting 结构来学习自适应的球面小波用于汇聚和反汇聚，以实现更高效的层次化特征学习。