Distributed Consensus for Global Matrix Formation in the Principal Component Pursuit Scenario

Gustavo Suárez , Juan David Velásquez

Research output: Contribution to journalArticle in an indexed scientific journalpeer-review


The aim behind principal component pursuit is to recover a low-rank matrix and a sparse matrix from a noisy signal which is the sum of both matrices. This optimization problem is a priori and non-convex and is useful in signal processing, data compression, image processing, machine learning, fluid dynamics, and more. Here, a distributed scheme described by a static undirected graph, where each agent only observes part of the noisy or corrupted matrix, is applied to achieve a consensus; then, a robust approach that can also handle missing values is applied using alternating directions to solve the convex relaxation problem, which actually solves the non-convex problem under some weak assumptions. Some examples of image recovery are shown, where the network of agents achieves consensus exponentially fast.

Original languageEnglish
Article number3619
JournalApplied Sciences (Switzerland)
Issue number9
StatePublished - May 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2024 by the authors.


  • consensus
  • image recovery
  • principal component pursuit
  • static graph


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