Pierre Vandergheynst

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This paper addresses the problem of mapping images between different vision sensors. Such a mapping could be modeled as a sampling problem that has to encompass the change of geometry between the two sensors and the specific discretization of the real scen ...

In this paper, we present an original non-linear subdivision scheme suitable for univariate data, plane curves and discrete triangulated surfaces, while keeping the complexity acceptable. The proposed technique is compared to linear subdivision methods having an identical support. Numerical criteria are proposed to verify basic properties, such as convergence of the scheme and the regularity of the limit function.

We advocate the use of a novel compressed sensing technique for accelerating the magnetic resonance image acquisition process, coined spread spectrum MR imaging or simply s2MRI. The method resides in pre-modulating the signal of interest by a linear chirp, ...

This paper introduces an area- and power-efficient approach for compressive recording of cortical signals used in an implantable system prior to transmission. Recent research on compressive sensing has shown promising results for sub-Nyquist sampling of sp ...

Sinal-processing on graphs has developed into a very active field of research during the last decade. In particular, the number of applications using frames con-structed from graphs, like wavelets on graphs, has substantially increased. To attain scalability for large graphs, fast graph-signal filtering techniques are needed. In this contribution, we propose an accelerated algorithm based on the Lanczos method that adapts to the Laplacian spectrum without explicitly computing it. The result is an accurate,

This paper introduces a novel algorithm for sparse approximation in redundant dictionaries called the M-term pursuit (MTP). This algorithm decomposes a signal into a linear combination of atoms that are selected in order to represent the main signal compon ...

How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard ...

A correlation function that compares each base in a DNA sequence to its various neighbours and which is subsequently processed by Fourier and wavelet transforms has been developed. The procedure has been applied to sequences from the human chromosome 22, to nef genes from various HIV clones and to myosin heavy chain DNA. It permits to readily visualize regular features in DNA which are related to the stability of heteroduplexes formed upon strand slippage.

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we propose ShapeNet, a generalization of the popular convolutional neural networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of

A generic approach is presented to detect and track people with a network of fixed and omnidirectional cameras given severely degraded foreground silhouettes. The problem is formulated as a sparsity constrained inverse problem. A dictionary made of atoms representing the presence of a person at a given location is used within the problem formulation. A re- weighted scheme is considered to better approximate the sparsity prior. Although the framework is generic to any scene, the focus of this paper is to eva

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic topology of the graph data ...

We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random modulation, con ...

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal e ...

Sparse approximation using redundant dictionaries is an efficient tool for many applications in the field of signal processing. The performances largely depend on the adaptation of the dictionary to the signal to decompose. As the statistical dependencies are most of the time not obvious in natural high-dimensional data, learning fundamental patterns is an alternative to analytical design of bases and has become a field of acute research. Most of the time, the underlying patterns of a class of signals can b

Assume a multichannel data matrix, which due to the column-wise dependencies, has low-rank and joint-sparse representation. This matrix wont have many degrees of freedom. Enormous developments over the last decade in areas of compressed sensing and low-rank matrix recovery, let us thinking of acquiring the whole matrix elements from very few non-adaptive linear measurements. This paper attempts to answer the following questions: what should be those measurements? How to design a computationally tractable al

The effective representation of the structures in the multiview images is an important problem that arises in visual sensor networks. This paper presents a novel recovery scheme from compressive samples which exploit local and non-local correlated structures in dense multiview images. The recovery model casts into convex minimization framework which penalizes the sparse and low-rank constraints on the data. The sparsity constraint models the correlations among pixels in a single image whereas the global cor

In this article is shown that with high probability the thresholding algorithm can recover signals that are sparse in a redundant dictionary as long as the {\it 2-Babel function} is growing slowly. This implies that it can succeed for sparsity levels up to ...

An instrumented falling weight impact test is thoroughly investigated in two cases, that of a rebound and that of a rupture in the sample. First, the force signal is analyzed with four methods: the continuous wavelet transform (with different wavelets: derivatives of a Gaussian and Morlet's), the Gabor transform, the Wigner Ville transform and the classical Fourier analysis. It is shown how a proper use of the time frequency methods allows to precisely detect the discontinuities in the signal, the moment of

This paper presents a new image representation method based on anisotropic refinement. It has been shown that wavelets are not optimal to code 2-D objects which need true 2-D dictionaries for efficient approximation. We propose to use rotations and anisotropic scaling to build a real bi-dimensional dictionary. Matching Pursuit then stands as a natural candidate to provide an image representation with an anisotropic refinement scheme. It basically decomposes the image as a series of basis functions weighted

In recent years, many works on geometric image representation have appeared in the literature. Geometric video representation has not received such an important attention so far, and only some initial works in the area have been presented. Works on geometr ...

Pierre Vandergheynst

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TV-Regularized Generation of Planar Images from Omnicams

Non-linear subdivision using local spherical coordinates

Accelerated MR imaging with spread spectrum encoding

Compact Low-Power Cortical Recording Architecture for Compressive Multichannel Data Acquisition

MATHICSE Technical Report : Accelerated filtering on graphs using Lanczos method

Sparse Approximation Using M-Term Pursuit and Application in Image and Video Coding

Spectrally approximating large graphs with smaller graphs

Fourier and wavelet transform analysis, a tool for visualising regular patterns in DNA

ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds

Sport Players Detection and Tracking With a Mixed Network of Planar and Omnidirectional Cameras

A Multiscale Pyramid Transform for Graph Signals

Universal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques

Generalised Implicit Neural Representations

Learning redundant dictionaries with translation invariance property: the MoTIF algorithm

Guaranteed recovery of a low-rank and joint-sparse matrix from incomplete and noisy measurements

Joint Low-rank and Sparse Light Field Modeling for Dense Multiview Data Compression

Average Performance Analysis for Thresholding

Modeling and simulation of an impact test using wavelets, analytical solutions and finite elements

Efficient image representation by anisotropic refinement in Matching Pursuit

Geometric Video Approximation Using Weighted Matching Pursuit