Paulo Sanches Gonçalves - Academia.edu (original) (raw)
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Universidad Nacional de Ingeneria
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Papers by Paulo Sanches Gonçalves
System Dynamics Review, 2010
Cooperative and Graph Signal Processing
Design of graph filters and filterbanks concepts underlying such filters and representations of g... more Design of graph filters and filterbanks concepts underlying such filters and representations of graph signals. We first recall the different Graph Fourier Transforms that have been developed in the literature, and show how to introduce a notion of frequency analysis for graph signals by looking at their variations. Then, we move to the introduction of graph filters, that are defined like the classical equivalent for 1D signals or 2D images, as linear systems which operate on each frequency of a signal. Some examples of filters and of their implementations are given. Finally, as alternate representations of graph signals, we focus on multiscale transforms that are defined from filters. Continuous multiscale transforms such as spectral wavelets on graphs are reviewed, as well as the versatile approaches of filterbanks on graphs. Several variants of graph filterbanks are discussed, for structured as well as arbitrary graphs, with a focus on the central point of the choice of the decimation or aggregation operators.
Comptes Rendus Physique
The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that is ... more The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that is the Fourier Transform. The flexibility of this analysis, its computational efficiency and the physical interpretation it offers makes it a cornerstone in many scientific domains. With the explosion of digital data, both in quantity and diversity, the generalization of the tools based on Fourier Transform is mandatory. In data science, new problems arose for the processing of irregular data such as social networks, biological networks or other data on networks. Graph Signal Processing is a promising approach to deal with those. The present text is an overview of the state-of-the-art in Graph Signal Processing, focusing on how to define a Fourier Transform for data on graphs, how to interpret it and how to use it to process such data. It closes showing some examples of use. Along the way, the review reveals how Fourier's work remains modern and universal, and how his concepts, coming from physics and blended with mathematics, computer science and signal processing, play a key role to answer the modern challenges in data science.
System Dynamics Review, 2010
Cooperative and Graph Signal Processing
Design of graph filters and filterbanks concepts underlying such filters and representations of g... more Design of graph filters and filterbanks concepts underlying such filters and representations of graph signals. We first recall the different Graph Fourier Transforms that have been developed in the literature, and show how to introduce a notion of frequency analysis for graph signals by looking at their variations. Then, we move to the introduction of graph filters, that are defined like the classical equivalent for 1D signals or 2D images, as linear systems which operate on each frequency of a signal. Some examples of filters and of their implementations are given. Finally, as alternate representations of graph signals, we focus on multiscale transforms that are defined from filters. Continuous multiscale transforms such as spectral wavelets on graphs are reviewed, as well as the versatile approaches of filterbanks on graphs. Several variants of graph filterbanks are discussed, for structured as well as arbitrary graphs, with a focus on the central point of the choice of the decimation or aggregation operators.
Comptes Rendus Physique
The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that is ... more The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that is the Fourier Transform. The flexibility of this analysis, its computational efficiency and the physical interpretation it offers makes it a cornerstone in many scientific domains. With the explosion of digital data, both in quantity and diversity, the generalization of the tools based on Fourier Transform is mandatory. In data science, new problems arose for the processing of irregular data such as social networks, biological networks or other data on networks. Graph Signal Processing is a promising approach to deal with those. The present text is an overview of the state-of-the-art in Graph Signal Processing, focusing on how to define a Fourier Transform for data on graphs, how to interpret it and how to use it to process such data. It closes showing some examples of use. Along the way, the review reveals how Fourier's work remains modern and universal, and how his concepts, coming from physics and blended with mathematics, computer science and signal processing, play a key role to answer the modern challenges in data science.