## Abstract

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 language | English |
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Article number | 3619 |

Journal | Applied Sciences (Switzerland) |

Volume | 14 |

Issue number | 9 |

DOIs | |

State | Published - May 2024 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2024 by the authors.

## Keywords

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