Non-Bayesian Estimation Framework for Signal Recovery on Graphs

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Graph signals arise from physical networks, such as power and communication systems, or as a result of a convenient representation of data with complex structure, such as social networks. We consider the problem of general graph signal recovery from noisy, corrupted, or incomplete measurements and under structural parametric constraints, such as smoothness in the graph frequency domain. In this paper, we formulate the graph signal recovery as a non-Bayesian estimation problem under a weighted mean-squared-error (WMSE) criterion, which is based on a quadratic form of the Laplacian matrix of the graph, and its trace WMSE is the Dirichlet energy of the estimation error w.r.t. the graph. The Laplacian-based WMSE penalizes estimation errors according to their graph spectral content and is a difference-based cost function which accounts for the fact that in many cases signal recovery on graphs can only be achieved up to a constant addend. We develop a new Cramér-Rao bound (CRB) on the Laplacian-based WMSE and present the associated Lehmann unbiasedness condition w.r.t. the graph. We discuss the graph CRB and estimation methods for the fundamental problems of 1) a linear Gaussian model with relative measurements; and 2) bandlimited graph signal recovery. We develop sampling allocation policies that optimize sensor locations in a network for these problems based on the proposed graph CRB. Numerical simulations on random graphs and on electrical network data are used to validate the performance of the graph CRB and sampling policies.

Original languageEnglish
Article number9340602
Pages (from-to)1169-1184
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume69
DOIs
StatePublished - 1 Jan 2021

Keywords

  • Dirichlet energy
  • Laplacian matrix
  • Non-Bayesian parameter estimation
  • graph Cramér-Rao bound
  • graph signal processing
  • graph signal recovery
  • sensor placement

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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