inria-00369562, version 1
Basis Identification from Random Sparse Samples
SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations (2009)
- a – INRIA
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http://www.inria.fr/equipes/metiss
CNRS : UMR6074 – INRIA – Institut National des Sciences Appliquées (INSA) - Rennes – Université de Rennes 1 Campus de Beaulieu 35042 Rennes cedex France - 2:
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École Polytechnique Fédérale de Lausanne EPFL, 1015 Lausanne Switzerland
Bibliographic reference
- Type of document: Peer-reviewed conferences/proceedings
- Domain:
Computer Science/Signal and Image Processing Engineering Sciences/Signal and Image processing - Title: Basis Identification from Random Sparse Samples
- Abstract: This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via ℓ1-minimisation. The problem is to identify a dictionary [\Phi] from a set of training samples Y knowing that [Y = \PhiX] for some coefficient matrix X. Using a characterisation of coefficient matrices X that allow to recover any basis as a local minimum of an ℓ1-minimisation problem, it is shown that certain types of sparse random coefficient matrices will ensure local identifiability of the basis with high probability. The typically sufficient number of training samples grows up to a logarithmic factor linearly with the signal dimension.
- Full text language: English
- Publication date: 2009
- Audience: international
- Conference title: SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations
- Conference city: Saint Malo
- Country: France
- Conference date: 2009-04-06
- Organizer: Inria Rennes - Bretagne Atlantique
- Scientific editor(s): Rémi Gribonval
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- inria-00369562, version 1
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- oai:hal.inria.fr:inria-00369562
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- Submitted on: Tuesday, 24 March 2009 11:25:57
- Updated on: Tuesday, 24 March 2009 11:50:05
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