353 citations · 1.8k across the 69 of their papers we have counts for
16 papers · 1 filter
Continuous dictionaries meet low-rank tensor approximations
Clement Elvira, Jeremy E. Cohen, Cedric Herzet +1
In this short paper we bridge two seemingly unrelated sparse approximation topics: continuous sparse coding and low-rank approximations. We show that for a specific choice of conti…
When does OMP achieve exact recovery with continuous dictionaries?
Clément Elvira, Rémi Gribonval, Charles Soussen +1
This paper presents new theoretical results on sparse recovery guarantees for a greedy algorithm, Orthogonal Matching Pursuit (OMP), in the context of continuous parametric diction…
Is the 1-norm the best convex sparse regularization?
Yann Traonmilin, Samuel Vaiter, Rémi Gribonval
The 1-norm is a good convex regularization for the recovery of sparse vectors from under-determined linear measurements. No other convex regularization seems to surpass its sparse…
Instance Optimal Decoding and the Restricted Isometry Property
Nicolas Keriven, Rémi Gribonval
In this paper, we address the question of information preservation in ill-posed, non-linear inverse problems, assuming that the measured data is close to a low-dimensional model se…
Sketched Clustering via Hybrid Approximate Message Passing
Evan Byrne, Antoine Chatalic, Remi Gribonval +1
In sketched clustering, a dataset of samples is first sketched down to a vector of modest size, from which the centroids are subsequently extracted. Advantages include i) reduc…
Beyond Moore-Penrose Part II: The Sparse Pseudoinverse
Ivan Dokmanić, Rémi Gribonval
This is the second part of a two-paper series on generalized inverses that minimize matrix norms. In Part II we focus on generalized inverses that are minimizers of entrywise p nor…
Beyond Moore-Penrose Part I: Generalized Inverses that Minimize Matrix Norms
Ivan Dokmanić, Rémi Gribonval
This is the first paper of a two-long series in which we study linear generalized inverses that minimize matrix norms. Such generalized inverses are famously represented by the Moo…
Compressed sensing in Hilbert spaces
Yann Traonmilin, Gilles Puy, Rémi Gribonval +1
In many linear inverse problems, we want to estimate an unknown vector belonging to a high-dimensional (or infinite-dimensional) space from few linear measurements. To overcome the…
Stable recovery of low-dimensional cones in Hilbert spaces: One RIP to rule them all
Yann Traonmilin, Rémi Gribonval
Many inverse problems in signal processing deal with the robust estimation of unknown data from underdetermined linear observations. Low dimensional models, when combined with appr…
Recipes for stable linear embeddings from Hilbert spaces to R^m
Gilles Puy, Mike Davies, Rémi Gribonval
We consider the problem of constructing a linear map from a Hilbert space (possibly infinite dimensional) to that satisfies a restricted isometry prope…
Fundamental performance limits for ideal decoders in high-dimensional linear inverse problems
Anthony Bourrier, Mike E. Davies, Tomer Peleg +2
This paper focuses on characterizing the fundamental performance limits that can be expected from an ideal decoder given a general model, ie, a general subset of "simple" vectors o…
Convex Optimization Approaches for Blind Sensor Calibration using Sparsity
Cagdas Bilen, Gilles Puy, Rémi Gribonval +1
We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using me…
Exact Recovery Conditions for Sparse Representations with Partial Support Information
C. Herzet, C. Soussen, J. Idier +1
We address the exact recovery of a k-sparse vector in the noiseless setting when some partial information on the support is available. This partial information takes the form of ei…
Coherence-based Partial Exact Recovery Condition for OMP/OLS
Cedric Herzet, Charles Soussen, Jerome Idier +1
We address the exact recovery of the support of a k-sparse vector with Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) in a noiseless setting. We consider the…
Universal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques
Gilles Puy, Pierre Vandergheynst, Rémi Gribonval +1
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…
Dictionary Identification - Sparse Matrix-Factorisation via -Minimisation
Remi Gribonval, Karin Schnass
This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via -minimisation. The problem can also be seen as facto…