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Wavelets on graphs via spectral graph theory

Publications associées (58)

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A Spectral Method for Generating Surrogate Graph Signals

Dimitri Nestor Alice Van De Ville, Elvira Pirondini, Martina Coscia, Anna Vybornova

The increasing availability of network data is leading to a growing interest in processing of signals on graphs. One notable tool for extending conventional signal-processing operations to networks is the graph Fourier transform that can be obtained as the ...

Institute of Electrical and Electronics Engineers2016

Multilinear Low-Rank Tensors on Graphs & Applications

Pierre Vandergheynst, Nauman Shahid, Francesco Grassi

We propose a new framework for the analysis of low- rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank S ...

2016

Optimal Window and Lattice in Gabor Transform. Application to Audio Analysis.

Benjamin Ricaud

This article deals with the use of optimal lattice and optimal window in Discrete Gabor Transform computation. In the case of a generalized Gaussian window, extending earlier contributions, we introduce an additional local window adaptation technique for n ...

Ieee2016

A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

Kyong Hwan Jin

Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered as two distinct reconstruction problems. Inspired by recent k-space interpolation methods, an annihilating filter-based low-rank Hankel matrix approach is proposed as a general fr ...

IEEE2016

Divergence-Free Wavelet Frames

Michaël Unser, Emrah Bostan, John Paul Ward

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Fast Detection and Refined Scale Estimation Using Complex Isotropic Wavelets

Michaël Unser, Daniel Sage, Zsuzsanna Püspöki, John Paul Ward

The dyadic scaling in the discrete wavelet transform can lead to a loss of precision, in comparison to the computationally unrealistic continuous wavelet transform. To overcome this obstacle, we propose a novel method to locally scale wavelets between dyad ...

IEEE2015

Graph-based Image Inpainting

Michaël Defferrard

The project goal was to explore the applications of spectral graph theory to address the inpainting problem of large missing chunks. We used a non-local patch graph representation of the image and proposed a structure detector which leverages the graph rep ...

2014

On sums of graph eigenvalues

Joachim Stubbe

We use two variational techniques to prove upper bounds for sums of the lowest several eigenvalues of matrices associated with finite, simple, combinatorial graphs. These include estimates for the adjacency matrix of a graph and for both the standard combi ...

Elsevier Science Inc2014

Multiscale Centerline Detection by Learning a Scale-Space Distance Transform

Pascal Fua, Vincent Lepetit, Amos Sironi

We propose a robust and accurate method to extract the centerlines and scale of tubular structures in 2D images and 3D volumes. Existing techniques rely either on filters designed to respond to ideal cylindrical structures, which lose accuracy when the lin ...

2014

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

Michaël Unser

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transform ...

Siam Publications2013