Pierre Vandergheynst

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This paper presents a new scalable and highly flexible color image coder based on a Matching Pursuit expansion. The Matching Pursuit algorithm provides an intrinsically progressive stream and the proposed coder allows us to reconstruct color information from the first bit received. In order to efficiently capture edges in natural images, the dictionary of atoms is built by translation, rotation and anisotropic refinement of a wavelet-like mother function. This dictionary is moreover invariant under shifts a

In our previous work, tracking the iso-level sets through total variation scale-space proved to be a very efficient tool for unsupervised segmentation. Stepping on these results, we propose a new segmentation approach in a unified total variation framework. The main idea is to use the total variation energy at each scale to drive the region merging process. We show that this total variation formulation, which was originally proposed for restoration and enhancement, is also well suited for segmentation. In a

A method is disclosed for decomposing a set of even and odd pictures into low-band and high-band pictures respectively in a image decomposing unit, in which the even picture is used by at least two prediction motion compensators on which the output signal ...

We propose a method for signal reconstruction in semi-parametric dictionaries. The proposed algorithm estimates both the signal decomposition and the intrinsic parameters of the dictionary during the reconstruction process. Theoretical results about the convergence of the algorithm are presented. The method is used here for joint reconstruction of misaligned images.

In this article we present a signal model for classification based on a collection of low dimensional subspaces embedded into the high dimensional signal space. We develop an alternate projection algorithm to find such a collection and finally test the cla ...

This paper presents a progressive coding scheme for 3-D objects, based on overcomplete signal expansions on the 2-D sphere. Due to increased freedom in the basis construction, redundant expansions have shown interesting approximation properties in the deco ...

Using a low-level representation of images, like matching pursuit, we introduce a new way of describing objects through a general description using a translation, rotation, and isotropic scale invariant dictionary of basis functions. We then use this description as a predefined dictionary of the object to conduct a shape recognition task. We show some promising results for the detection with simple shapes.

This article does not present new mathematical results, it solely aims at discussing some numerical experiments with MALDI Imaging data. However, these experiments are based on and could not be done without the mathematical results obtained in the UNLocX p ...

The work presented in this paper extends the concept of sub-band video coding based on a 3D wavelet transform to a more adaptive approach. A formal comparison is presented between the performances inferred by the use of the 3D wavelet transform and the use of a 2D wavelet in the spatial domain extended by a locally adaptive transform in the temporal dimension. Some advantages are foreseen for the new scheme since it is able to better deal with certain signal models like appearing and moving edges. An increa

With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS) techniques, which e ...

This paper presents a novel approach to capture light field in camera arrays based on the compressive sensing framework. Light fields are captured by a linear array of cameras with overlapping field of view. In this work, we design a redundant dictionary to exploit cross-cameras correlated structures in order to sparsely represent cameras image. We show experimentally that the projection of complex synthetic scenes into the designed dictionary yield very sparse coefficients.

In this paper, we focus on the use of random projections as a dimensionality reduction tool for sampled manifolds in high-dimensional Euclidean spaces. We show that geodesic paths approximations from nearest neighbors Euclidean distances are well-preserved ...

In this technical report the Discrete Wavelet Frames are build on the already existing Spherical Continuous Wavelet Transform. The spherical half-continuous frames are explored, i.e when the position on the sphere is kept continuous variable. Then, the controlled frames are introduced, which comes from the particular nature of the underlying theory, namely the conflict between dilation and the compacity of the spherical manifold. The perspectives for the future work are given.

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address ...

We propose a novel method to automatically detect and extract the video modality of the sound sources that are present in a scene. For this purpose, we first assess the synchrony between the moving objects captured with a video camera and the sounds record ...

Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the ...

We study the problem of matrix completion when infor- mation about row or column proximities is available, in the form of weighted graphs. The problem can be formulated as the optimization of a convex function that can be solved efficiently using the alternating direction multipliers method. Experiments show that our model offers better reconstruction than the standard method that only uses a low rank assumption, especially when few observations are available.

In this report we propose a new coding scheme based on the Matching Pursuit algorithm and exploiting some of the new features introduced by H.264 for motion estimation. Main points of this work are the design of a redundant dictionary suitable for coding displaced frame dierences, the use of fast techniques for atom selection, which work in the Fourier domain and exploit the spatial localization of the atoms, the adaptive coding scheme aimed at optimizing the resouce allocation for transmitting the atom par

Real-world phenomena involve complex interactions between multiple signal modalities. As a consequence, humans are used to integrate at each instant perceptions from all their senses in order to enrich their understanding of the surrounding world. This par ...

Pierre Vandergheynst

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Color image scalable coding with Matching Pursuit

An Adaptive Total Variation Model for Image Segmentation

Image transform for video coding

Color Image Scalable Coding with Matching Pursuit

Robust joint reconstruction of misaligned images using semi-parametric dictionaries

Classification via Incoherent Subspaces

Progressive Coding of 3-D Objects Based on Overcomplete Decompositions

Rotation and scale invariant shape representation and recognition using Matching Pursuit

Numerical experiments with MALDI Imaging data

Locally Temporal Adaptive Transform Scheme for Sub-band Video Coding

Compressive Source Separation: Theory and Methods for Hyperspectral Imaging

Light Field Compressive Sensing

On the estimation of geodesic paths on sampled manifolds under random projections

Stereographic Frames of Wavelets on the Sphere

Clustering with Multi-Layer Graphs: A Spectral Perspective

Unsupervised Extraction of Audio-Visual Objects

Correspondence principle between spherical and Euclidean wavelets

Enhanced Matrix Completion with Manifold Learning

Hybrid video coding using bi-dimensional matching pursuit

Learning Multi-Modal Dictionaries