Accelerated graph-based spectral polynomial filters
This work addresses efficiency improvements for graph signal processing, but it appears incremental as it builds on existing polynomial filtering methods.
The authors tackled the computational cost of graph-based spectral denoising by proposing accelerated polynomial filters using flexible Krylov subspace solvers like LOBPCG, resulting in faster filtering without specifying concrete speed-up numbers.
Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the bilateral and guided filters. We propose constructing accelerated polynomial filters by running flexible Krylov subspace based linear and eigenvalue solvers such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG) method.