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Sequential Minimal Eigenvalues - An Approach to Analysis Dictionary Learning

Boaz Ophir 1 Michael Elad 1 Nancy Bertin 2 Mark D. Plumbley 3
2 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : Over the past decade there has been a great interest in asynthesis-based model for signals, based on sparse and re-dundant representations. Such a model assumes that the sig-nal of interest can be decomposed as a linear combinationof few columns from a given matrix (the dictionary). An al-ternative, analysis-based, model can be envisioned, where ananalysis operator multiplies the signal, leading to a sparseoutcome. In this paper we propose a simple but effectiveanalysis operator learning algorithm, where analysis "atoms"are learned sequentially by identifying directions that are or-thogonal to a subset of the training data. We demonstratethe effectiveness of the algorithm in three experiments, treat-ing synthetic data and real images, showing a successful andmeaningful recovery of the analysis operator.
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https://hal.inria.fr/inria-00577231
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Submitted on : Thursday, September 15, 2011 - 12:02:48 PM
Last modification on : Wednesday, June 16, 2021 - 3:41:29 AM
Long-term archiving on: : Friday, December 16, 2011 - 2:20:19 AM

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  • HAL Id : inria-00577231, version 1

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Boaz Ophir, Michael Elad, Nancy Bertin, Mark D. Plumbley. Sequential Minimal Eigenvalues - An Approach to Analysis Dictionary Learning. The 19th European Signal Processing Conference (EUSIPCO‐2011), Aug 2011, Barcelona, Spain. ⟨inria-00577231⟩

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