Vector-Valued Graph Trend Filtering with Non-Convex Penalties

Rohan Varma, Harlin Lee, Jelena Kovacevic, Yuejie Chi

Research output: Contribution to journalArticle

Abstract

This article studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising vector-valued graph signals with a family of non-convex regularizers, which exhibit superior recovery performance over existing convex regularizers. Using an oracle inequality, we establish the statistical error rates of first-order stationary points of the proposed non-convex method for generic graphs. Furthermore, we present an ADMM-based algorithm to solve the proposed method and establish its convergence. Numerical experiments are conducted on both synthetic and real-world data for denoising, support recovery, event detection, and semi-supervised classification.

Original languageEnglish (US)
Article number8926407
Pages (from-to)48-62
Number of pages15
JournalIEEE Transactions on Signal and Information Processing over Networks
Volume6
DOIs
StatePublished - Jan 1 2020

Keywords

  • Graph signal processing
  • graph trend filtering
  • non-convex optimization
  • semi-supervised classification

ASJC Scopus subject areas

  • Signal Processing
  • Information Systems
  • Computer Networks and Communications

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