# \'Echantillonnage de signaux sur graphes via des processus d\'eterminantaux

## TL;DR

This paper introduces a novel sampling strategy for k-bandlimited graph signals using determinantal point processes, enabling efficient reconstruction with fewer samples without full Laplacian diagonalization.

## Contribution

It proposes a new method based on determinantal point processes for sampling graph signals, avoiding costly Laplacian diagonalization and improving sampling efficiency.

## Key findings

- Reconstruction with only O(k) samples is possible.
- The proposed sampling algorithm is faster than existing methods by an order of k.
- The method avoids partial diagonalization of the graph Laplacian.

## Abstract

We consider the problem of sampling k-bandlimited graph signals, ie, linear combinations of the first k graph Fourier modes. We know that a set of k nodes embedding all k-bandlimited signals always exists, thereby enabling their perfect reconstruction after sampling. Unfortunately, to exhibit such a set, one needs to partially diagonalize the graph Laplacian, which becomes prohibitive at large scale. We propose a novel strategy based on determinantal point processes that side-steps partial diagonalisation and enables reconstruction with only O(k) samples. While doing so, we exhibit a new general algorithm to sample determinantal process, faster than the state-of-the-art algorithm by an order k.