Hierarchical Spherical CNNs with Lifting-based Adaptive Wavelets for Pooling and Unpooling
This work addresses a domain-specific problem for researchers and practitioners in spherical signal processing, offering an incremental improvement over existing methods by enhancing feature learning efficiency.
The paper tackles the problem of information loss in pooling and unpooling operations for hierarchical spherical CNNs by proposing a novel framework, LiftHS-CNN, which uses a learnable lifting structure to adaptively generate spherical wavelets, resulting in improved performance on various spherical domain tasks as validated by empirical evaluations.
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.