Hierarchical Spherical CNNs With Lifting-Based Adaptive Wavelets for Pooling and Unpooling.

Area of Science:

• Computer Science
• Artificial Intelligence
• Signal Processing

Background:

• Hierarchical spherical convolutional neural networks (HS-CNNs) are crucial for processing spherical data.
• Existing pooling methods in HS-CNNs cause information loss and spectral distortion.
• Unpooling methods can alter original signal spectra.

Purpose of the Study:

• To develop a novel framework for HS-CNNs that addresses limitations in pooling and unpooling.
• To introduce adaptive spherical wavelets for improved information preservation and spectral fidelity.
• To enhance the performance of HS-CNNs on various spherical data tasks.

Main Methods:

• Proposed LiftHS-CNNs framework utilizing a lifting structure to learn adaptive spherical wavelets.
• Developed pooling operation that adaptively partitions signals into frequency sub-bands, preserving low-frequency information.
• Introduced an invertible unpooling operation to restore signals while maintaining spectral characteristics.
• Employed graph attention for learnable update and predict operators within the lifting structure.

Main Results:

• LiftHS-CNNs demonstrated superior performance compared to existing methods on benchmark spherical datasets.
• The proposed pooling and unpooling operations effectively preserve spatial locality, vanishing moments, and stability.
• Learned spherical wavelets adapt to different signal spectra and task requirements, minimizing information loss.
• Experiments confirmed the framework's ability to preserve spectral characteristics during signal reconstruction.

Conclusions:

• LiftHS-CNNs offer a significant advancement in HS-CNNs by enabling adaptive pooling and unpooling.
• The lifting-structure-based approach effectively addresses information loss and spectral distortion issues.
• The proposed method shows broad applicability and superiority across diverse spherical data processing tasks.