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Two Papers by Benjamin Girault Published as Part of ICASSP 2021 

Two papers co-authored by Benjamin Girault, an Assistant Professor in Computer Science and a researcher at CREST, have been published on the occasion of the 2021 edition of the International Conference on Acoustics, Speech and Signal Processing (ICASSP).  

The International Conference on Accoustics, Speech and Signal Processing (ICASSP) is the IEEE Signal Processing Society’s flagship conference on signal processing and its applications. The 46th edition of ICASSP is virtually held from Toronto, Canada from June 6th to 11th.

These two papers belong to the field of Graph Signal Processing (GSP), for which arbitrarily structured data is considered. Benjamin Girault and his co-authors from the University of Southern California (USA) and the Autonomous University of Barcelona (Spain) propose new transforms useful for analysis and transformation of such data. Topical applications include image compression (to introduce new methods for storing efficiently images) and point cloud compression (e.g. to store and send efficiently point representations of 3D scenes, with colors, for autonomous vehicles, 3D video conferencing, or topographic mapping).

Spectral folding and two-channel filter-banks on arbitrary graphs

Authors: Eduardo Pavez, Benjamin Girault, Antonio Ortega, Philip A. Chou

In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction, orthogonality and bi-orthogonality conditions in the graph spectral domain resemble those for traditional filter-banks. Therefore, many of the well-known orthogonal and bi-orthogonal designs can be easily adapted for graph signals. A major limitation is that this framework can only be applied to the normalized Laplacian of bipartite graphs. In this paper we extend this theory to arbitrary graphs and positive semi-definite variation operators. Our approach is based on a different definition of the graph Fourier transform (GFT), where orthogonality is defined with respect to the Q inner product. We construct GFTs satisfying a spectral folding property, which allows us to easily construct orthogonal and bi-orthogonal perfect reconstruction filter-banks. We illustrate signal representation and computational efficiency of our filter-banks on 3D point clouds with hundreds of thousands of points.

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Orthogonality and Zero DC Tradeoffs in Biorthogonal Graph Filterbanks

Authors: Dion E. O. Tzamarias, Eduardo Pavez, Benjamin Girault, Antonio Ortega, Ian Blanes, Joan Serra-Sagristà

Biorthogonal graph wavelet filterbanks, also known as GraphBior, are one of the most popular graph transforms used in image compression, but up to now, they could be designed based on two known admissible fundamental matrices: i) the random walk Laplacian, which heavily penalizes low degree pixels, and ii) the normalized Laplacian, which lacks a zero-DC response. By exploiting a new extension of the admissibility condition in GraphBior we propose a new fundamental matrix with the goal of distributing the errors of GraphBior more uniformly across pixels with different node degrees. Furthermore the proposed matrix preserves high energy compaction linked to the zero-DC GraphBior variation.

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Find out more about Benjamin Girault and research at ENSAI