What question did this study set out to answer?

This research aims to develop an intrinsic lifting scheme for processing quaternion signals on graphs, focusing on geometric relationships.

June 4, 2026Open Access

Intrinsic Lifting Scheme for Quaternion Graph Signals via Relative Rotation Adaptive Filtering

Key Points

This research aims to develop an intrinsic lifting scheme for processing quaternion signals on graphs, focusing on geometric relationships.
A single geometric quantity, the geodesic correlation, is used for graph construction and node partitioning.
Spherical shell sectors group neighbors based on rotation characteristics and use a B-spline kernel for weighting.
Prediction utilizes axis-angle formulas without typical log/exp maps, emphasizing intrinsic processing.
The proposed method demonstrates improved prediction accuracy compared to traditional methods, leveraging geometric proximity.
Using geodesic correlation significantly enhances the node partitioning process in quaternion-based graph signals.

Abstract

We introduced a lifting scheme for quaternion signals on that unifies graph construction, node partitioning, and prediction weights through a single geometric quantity—the geodesic correlation , the radial coordinate of the foliation of . Spherical shell sectors in the relative-rotation domain group coarse neighbors that share similar rotation magnitude and direction, and a tensor-product cubic B-spline kernel weights them by three-dimensional geometric proximity. Prediction is fully intrinsic—angles averaged as scalars, axes as unit vectors on , and the result reconstructed via the exact axis-angle formula, with no log/exp maps or Euclidean normalization.

Intrinsic Lifting Scheme for Quaternion Graph Signals via Relative Rotation Adaptive Filtering

Key Points

Abstract

Cite This Study

Also Consider

Also Consider