publications

2024

1. A New Branch-and-Bound Pruning Framework for \(\ell_0\)-Regularized Problems

   Théo Guyard, Cédric Herzet, Clément Elvira, and Ayse-Nur Arslan

   In Forty-first International Conference on Machine Learning (ICML), 2024

   arXiv

2023

1. Safe Peeling for \( \ell_0\)-Regularized Least-Squares

   Théo Guyard, Gilles Monnoyer, Clément Elvira, and Cédric Herzet

   In 31st European Signal Processing Conference (EUSIPCO), 2023

   DOI
2. One to beat them all: “RYU” – a unifying framework for the construction of safe balls

   T.-L. Tran, C. Elvira, H.-P. Dang, and C. Herzet

   2023

   arXiv
3. Safe Rules for the Identification of Zeros in the Solutions of the SLOPE Problem

   Clément Elvira, and Cédric Herzet

   SIAM Journal on Mathematics of Data Science, 2023

   DOI arXiv

2022

1. Bayes in action in deep learning and dictionary learning

   J. Arbel, H.-P. Dang, C. Elvira, C. Herzet, and 2 more authors

   In ESAIM: Proceedings and Surveys, 2022

   DOI
2. Node-Screening Tests For The L0-Penalized Least-Squares Problem

   T. Guyard, C. Herzet, and C. Elvira

   In ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2022

   DOI arXiv
3. Screen & Relax: Accelerating The Resolution Of Elastic-Net By Safe Identification of The Solution Support

   T. Guyard, C. Herzet, and C. Elvira

   In ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2022

   DOI arXiv
4. Region-free Safe Screening Tests for l1-penalized Convex Problems

   C. Herzet, C. Elvira, and H.-P. Dang

   In EURASIP European Signal Processing Conference (EUSIPCO), 2022

   DOI
5. Beyond GAP screening for Lasso by exploiting new dual cutting half-spaces

   T. L. Tran, C. Elvira, H.-P. Dang, and C. Herzet

   In EURASIP European Signal Processing Conference (EUSIPCO), 2022

   DOI arXiv

2021

1. When does OMP achieve exact recovery with continuous dictionaries?

   C. Elvira, R. Gribonval, C. Soussen, and C. Herzet

   Applied and Computational Harmonic Analysis, 2021

   DOI arXiv
2. Low-Rank Dynamic Mode Decomposition: An Exact and Tractable Solution

   P. Héas, and C. Herzet

   Journal of Nonlinear Science, 2021

   DOI arXiv

2020

1. Short and Squeezed: Accelerating the Computation of Antisparse Representations with Safe Squeezing

   C. Elvira, and C. Herzet

   In ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020

   DOI
2. Safe Squeezing for Antisparse Coding

   C. Elvira, and C. Herzet

   IEEE Transactions on Signal Processing, 2020

   DOI arXiv
3. Performance guarantees for a variational "multi-space" decoder

   C. Herzet, and M. Diallo

   Advances in Computational Mathematics, 2020

   DOI
4. Interpolating and translation-invariant approximations of parametric dictionaries

   F. Champagnat, and C. Herzet

   In 28th European Signal Processing Conference (EUSIPCO), 2020

   DOI arXiv

2019

1. Atom Selection in Continuous Dictionaries: Reconciling Polar and SVD Approximations

   F. Champagnat, and C. Herzet

   In ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019

   DOI
2. Region-based Relaxations to Accelerate Greedy Approaches

   C. Dorffer, C. Herzet, and A. Drémeau

   In 27th European Signal Processing Conference (EUSIPCO), 2019

   DOI
3. Gather and Conquer: Region-Based Strategies to Accelerate Safe Screening Tests

   C. Herzet, C. Dorffer, and A. Drémeau

   IEEE Transactions on Signal Processing, 2019

   DOI
4. OMP and continuous dictionaries: is k-step recovery possible?

   Clément Elvira, Rémi Gribonval, Charles Soussen, and Cédric Herzet

   In ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019

   DOI

2018

1. Model reduction from partial observations

   C. Herzet, P. Héas, and A. Drémeau

   International Journal for Numerical Methods in Engineering, 2018

   DOI arXiv
2. Joint Screening Tests for LASSO

   C. Herzet, and A. Drémeau

   In ICASSP 2018-IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2018

   DOI
3. Reduced Modeling of Unknown Trajectories

   P. Héas, and C. Herzet

   Archives of Computational Methods in Engineering, 2018

   DOI arXiv

2017

1. Optimal low-rank Dynamic Mode Decomposition

   P. Héas, and C. Herzet

   In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2017

   DOI arXiv

2016

1. A new approach for volume reconstruction in TomoPIV with the alternating direction method of multipliers

   Ioana Barbu, and Cédric Herzet

   Measurement Science and Technology, 2016

   Abs

   We adapt and import into the TomoPIV scenery a fast algorithm for solving the volume reconstruction problem. Our approach is based on the reformulation of the volume reconstruction task as a constrained optimization problem and the resort to the ‘alternating directions method of multipliers’ (ADMM). The inherent primal-dual algorithm is summarized in this article to solve the optimization problem related to the TomoPIV. In particular, the general formulation of the volume reconstruction problem considered in this paper allows one to: (i) take explicitly into account the level of the noise affecting the data; (ii) account for both the nonnegativity and the sparsity of the solution. Experiments on a numerical TomoPIV benchmark show that the proposed framework is a serious contender for the state-of-the-art.

2. Relaxed Recovery Conditions for OMP/OLS by Exploiting Both Coherence and Decay

   C. Herzet, A. Drémeau, and C. Soussen

   IEEE Transactions on Information Theory, 2016

   DOI
3. An Efficient Algorithm for Video Superresolution Based on a Sequential Model

   P. Héas, A. Drémeau, and C. Herzet

   SIAM Journal on Imaging Sciences, 2016

   DOI
4. Reduced-order modeling of hidden dynamics

   P. Héas, and C. Herzet

   In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016

   DOI
5. Safe screening tests for LASSO based on firmly non-expansiveness

   C. Herzet, and A. Malti

   In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Mar 2016

   DOI

2013

1. Joint k-Step Analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares

   C. Soussen, R. Gribonval, J. Idier, and C. Herzet

   IEEE Trans on Information Theory, Mar 2013

   DOI
2. Exact recovery conditions for sparse representations with partial support information

   C. Herzet, C. Soussen, J. Idier, and R. Gribonval

   IEEE Transactions on Information Theory, Mar 2013

   DOI

2012

1. Structured Bayesian Orthogonal Matching Pursuit

   A. Drémeau, C. Herzet, and L. Daudet

   In Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on, Mar 2012

   Abs DOI

   Taking advantage of the structures inherent in many sparse decompositions constitutes a promising research axis. In this paper, we address this problem from a Bayesian point of view. We exploit a Boltzmann machine, allowing to take a large variety of structures into account, and focus on the resolution of a joint maximum a posteriori problem. The proposed algorithm, called Structured Bayesian Orthogonal Matching Pursuit (SBOMP), is a structured extension of the Bayesian Orthogonal Matching Pursuit algorithm (BOMP) introduced in our previous work [1]. In numerical tests involving a recovery problem, SBOMP is shown to have good performance over a wide range of sparsity levels while keeping a reasonable computational complexity.

2. Boltzmann Machine and Mean-Field Approximation for Structured Sparse Decompositions

   A. Drémeau, C. Herzet, and L. Daudet

   Signal Processing, IEEE Transactions on, Mar 2012

   DOI