An Underparametrized Deep Decoder Architecture for Graph Signals

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.

arXiv commentThis paper has already been accepted on 2019 IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) and it is going to be published in its proceedings

References in corpus (8)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Geometric deep learning: going beyond Euclidean data
• Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
• Deep Image Prior
• Discrete Signal Processing on Graphs: Sampling Theory
• Convolutional Neural Network Architectures for Signals Supported on Graphs
• Sampling of graph signals with successive local aggregations
• Blind Identification of Graph Filters

Cited by in corpus (1)

• Untrained Graph Neural Networks for Denoising