# An Underparametrized Deep Decoder Architecture for Graph Signals

## TL;DR

This paper introduces a novel underparametrized deep decoder architecture tailored for graph signals, leveraging graph coarsening for improved reconstruction on irregular domains, outperforming traditional methods.

## Contribution

It generalizes untrained deep decoders to graph signals by integrating graph-aware upsampling and hierarchical clustering, enhancing reconstruction performance.

## Key findings

- Graph-aware upsampling improves reconstruction accuracy.
- Incorporating graph topology significantly outperforms methods ignoring structure.
- The approach is effective on both synthetic and real-world datasets.

## Abstract

While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform state-of-the-art methods in several tasks such as image compression and denoising. Motivated by the fact that many contemporary datasets have an irregular structure different from a 1D/2D grid, this paper generalizes untrained and underparametrized non-convolutional architectures to signals defined over irregular domains represented by graphs. The proposed architecture consists of a succession of layers, each of them implementing an upsampling operator, a linear feature combination, and a scalar nonlinearity. A novel element is the incorporation of upsampling operators accounting for the structure of the supporting graph, which is achieved by considering a systematic graph coarsening approach based on hierarchical clustering. The numerical results carried out in synthetic and real-world datasets showcase that the reconstruction performance can improve drastically if the information of the supporting graph topology is taken into account.