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Graph Laplacians for Rotation Equivariant Convolutional Neural Networks

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Graph Based Sinogram Denoising for Tomographic Reconstructions

Pierre Vandergheynst, Nauman Shahid

Limited data and low dose constraints are common problems in a variety of tomographic reconstruction paradigms which lead to noisy and incomplete data. Over the past few years sinogram denoising has become an essential pre-processing step for low dose Comp ...

2016

Combinations of adaptive filters: performance and convergence properties

Ali H. Sayed

Adaptive filters are at the core of many signal processing applications, ranging from acoustic noise supression to echo cancelation [1], array beamforming [2], channel equalization [3], to more recent sensor network applications in surveillance, target loc ...

IEEE2016

Accelerated Spectral Clustering Using Graph Filtering of Random Signals

Pierre Vandergheynst, Rémi Gribonval, Gilles Puy, Nicolas Tremblay

We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first

k

eigenvectors of the similarity matrix' Laplacian, whose computati ...

Ieee2016

A Precise Threshold For Quasi-Ramsey Numbers

János Pach

We consider the variation of Ramsey numbers introduced by Erdos and Pach [J. Graph Theory, 7 (1983), pp. 137-147], where instead of seeking complete or independent sets we only seek a t-homogeneous set, a vertex subset that induces a subgraph of minimum de ...

Siam Publications2015

Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames

Pierre Vandergheynst, David Shuman

We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph wavelet constructions ...

Institute of Electrical and Electronics Engineers2015

Laplacian Matrix Learning for Smooth Graph Signal Representation

Pascal Frossard, Pierre Vandergheynst, Xiaowen Dong

The construction of a meaningful graph plays a crucial role in the emerging field of signal processing on graphs. In this paper, we address the problem of learning graph Laplacians, which is similar to learning graph topologies, such that the input data fo ...

2015

Twin Photon Source: Spatio-temporal Properties

We propose a method to study and characterize the spatial and temporal properties of degenerate photon pairs emitted in SPDC, using a filtering system combined with temperature variation of the nonlinear crystal. The photons can be distinguished. We relate ...

Spie-Int Soc Optical Engineering2015

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

Homometric sets in trees

Radoslav Fulek, Slobodan Mitrovic

Let G = (V, E) denote a simple graph with vertex set V and edge set E. The profile of a vertex set V' subset of V denotes the multiset of pairwise distances between the vertices of V'. Two disjoint subsets of V are homometric if their profiles are the same ...

Academic Press Ltd- Elsevier Science Ltd2014

Inference of Mobility Patterns via Spectral Graph Wavelets