Deep Encoder-Decoder Neural Network Architectures for Graph Output Signals

Rey, Samuel; Tenorio, Víctor M.; Rozada, Sergio; Martino, Luca; Marqués, Antonio G.

doi:10.1109/ieeeconf44664.2019.9048908

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…The second architecture performs graph upsampling operations to progressively increase the size of the input until it matches the size of the observed signal. The upsampling operators are based on hierarchical clustering algorithms [15], [23]- [25] so that, in contrast with [26], matrix inversions are not required, avoiding the related numerical issues. Our work is substantially different from [15], [16], which deal with graph encoder-decoder architectures.…”

Section: Introductionmentioning

confidence: 99%

“…The upsampling operators are based on hierarchical clustering algorithms [15], [23]- [25] so that, in contrast with [26], matrix inversions are not required, avoiding the related numerical issues. Our work is substantially different from [15], [16], which deal with graph encoder-decoder architectures. On top of our theoretical analysis and extensive numerical simulations, additional differences to prior work are that: (a) our graph decoder is an untrained network, and thus, it does not need a training phase; (b) we only require a decoder-like architecture for denoising graph signals, so it is not necessary to jointly design and train two different architectures as done in [15], [16].…”

Section: Introductionmentioning

confidence: 99%

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Untrained Graph Neural Networks for Denoising

Rey¹,

Segarra²,

Heckel³

et al. 2021

Preprint

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A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important classes of signals are defined over irregular domains such as graphs. This paper introduces two untrained graph neural network architectures for graph signal denoising, provides theoretical guarantees for their denoising capabilities in a simple setup, and numerically validates the theoretical results in more general scenarios. The two architectures differ on how they incorporate the information encoded in the graph, with one relying on graph convolutions and the other employing graph upsampling operators based on hierarchical clustering. Each architecture implements a different prior over the targeted signals.To numerically illustrate the validity of the theoretical results and to compare the performance of the proposed architectures with other denoising alternatives, we present several experimental results with real and synthetic datasets.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Untrained Graph Neural Networks for Denoising

Rey¹,

Segarra²,

Heckel³

et al. 2021

Preprint

Self Cite

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show abstract

“…On the other hand, signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs, see [17]. For example, neural networks and graph signal processing have emerged as important actors in data-science applications dealing with complex datasets, see [18].…”

Section: Introductionmentioning

confidence: 99%