1. Multi-dimensional signal approximation with sparse structured priors using split Bregman iterations
- Author
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Michèle Sebag, Cédric Gouy-Pailler, Yoann Isaac, Quentin Barthélemy, Jamal Atif, Laboratoire d'analyse des données et d'intelligence des systèmes (LADIS), Département Métrologie Instrumentation & Information (DM2I), Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, TAckling the Underspecified (TAU), Laboratoire de Recherche en Informatique (LRI), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mensia Technologies [Rennes], Mensia Technologies [Paris], Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision (LAMSADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), The work presented in this paper has been partially funded by DIGITEO under the Grant 2011-053D, Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), CentraleSupélec-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and CentraleSupélec-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
FOS: Computer and information sciences ,Signal processing ,Optimization problem ,Noise reduction ,Computer Vision and Pattern Recognition (cs.CV) ,Computer Science - Computer Vision and Pattern Recognition ,02 engineering and technology ,Machine Learning (cs.LG) ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,Recovery ,Computer Science - Data Structures and Algorithms ,Prior probability ,Regularization ,0202 electrical engineering, electronic engineering, information engineering ,Data Structures and Algorithms (cs.DS) ,Electrical and Electronic Engineering ,Selection ,Image restoration ,Mathematics ,business.industry ,Linear Inverse Problems ,020206 networking & telecommunications ,Pattern recognition ,Sparse approximation ,[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] ,Regression ,Minimization ,Computer Science - Learning ,Image-Restoration ,Control and Systems Engineering ,Statistical analysis ,020201 artificial intelligence & image processing ,[SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC] ,Computer Vision and Pattern Recognition ,Decomposition method (constraint satisfaction) ,Artificial intelligence ,Minification ,Lasso ,business ,Software ,Algorithms ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
This paper addresses the structurally constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal regularization term is designed and used together with the standard ź 1 regularization term to enforce a sparse decomposition preserving the spatio-temporal structure of the signal. Secondly, an optimization algorithm based on the split Bregman approach is proposed to handle the associated optimization problem, and its convergence is analyzed. Our well-founded approach yields same accuracy as the other algorithms at the state of the art, with significant gains in terms of convergence speed. Thirdly, the empirical validation of the approach on artificial and real-world problems demonstrates the generality and effectiveness of the method. On artificial problems, the proposed regularization subsumes the Total Variation minimization and recovers the expected decomposition. On the real-world problem of electro-encephalography brainwave decomposition, the approach outperforms similar approaches in terms of P300 evoked potentials detection, using structured spatial priors to guide the decomposition. HighlightsA sparse structured decomposition method is proposed for multi-dimensional signals.Knowledge priors are encoded in a regularization to obtain plausible representations.The proposed split-Bregman based method outperforms counterparts in terms of speed.The approach is applied to EEG denoising for the extraction of P300 potentials.
- Published
- 2017