28 citations · 71 across the 9 of their papers we have counts for
7 papers · 1 filter
An algorithm for non-convex off-the-grid sparse spike estimation with a minimum separation constraint
Yann Traonmilin, Jean-François Aujol, Arhur Leclaire
Theoretical results show that sparse off-the-grid spikes can be estimated from (possibly compressive) Fourier measurements under a minimum separation assumption. We propose a pract…
The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension
Yann Traonmilin, Jean-François Aujol, Arthur Leclaire
Non-convex methods for linear inverse problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite…
The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem
Yann Traonmilin, Jean-François Aujol
The sparse spike estimation problem consists in estimating a number of off-the-grid impulsive sources from under-determined linear measurements. Information theoretic results ensur…
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…
Optimality of 1-norm regularization among weighted 1-norms for sparse recovery: a case study on how to find optimal regularizations
Yann Traonmilin, Samuel Vaiter
The 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measu…
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…