2024/08/26 by Matias de Jong van Lier, van Lier, Matias de Jong, Sebastián Elías Graiff Zurita +3
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced Data Compression Techniques #Algebraic Topology (math.AT) #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Neural Networks Stability and Synchronization #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2408.14109
openalex publication_date 2024/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study topology-based filtering of vertex-defined signals on graphs and their two-dimensional analogues. Unlike graph-spectral filters, the proposed approach distinguishes features by topological persistence rather than by spatial wavelength or periodicity. We consider graphs with faces embedded in surfaces, a class that includes discrete models of images and meshes. We prove that, in general, exact simultaneous removal of low-persistence features in dimensions 0 and 1 is impossible. This motivates a relaxed formulation, for which we introduce the Low Persistence Filter (LPF). The LPF removes finite-persistence features below a prescribed threshold while controlling the resulting ℓ_∞ perturbation of the signal. We illustrate the method on one-dimensional signals, two-dimensional images, and signals on triangular meshes. A Python implementation is publicly available.