Noise Aware Analysis Operator Learning For Approximately Cosparse Signals

Mehrdad Yaghoobi 1 Sangnam Nam 2 Rémi Gribonval 2 Michael Davies 3
1 Institute for Digital Communication Joint Research Institute for Signal & Image Processing School of Engineering and Electronics - University of Edinburgh
2 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
3 School of Engineering - University of Edinburgh
Abstract : This paper investigates analysis operator learning for the recently introduced cosparse signal model that is a natural analysis complement to the more traditional sparse signal model. Previous work on such analysis operator learning has relied on access to a set of clean training samples. Here we introduce a new learning framework which can use training data which is corrupted by noise and/or is only approximately cosparse. The new model assumes that a p-cosparse signal exists in an epsilon neighborhood of each data point. The operator is assumed to be uniformly normalized tight frame (UNTF) to exclude some trivial operators. In this setting, an alternating optimization algorithm is introduced to learn a suitable analysis operator.
Keywords : Sparse Approximation Analysis Framework Cosparse Signal Model Analysis Operator Learning Douglas- Rachford Splitting
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Conference papers
ICASSP - IEEE International Conference on Acoustics, Speech, and Signal Processing - 2012, Mar 2012, Kyoto, Japan. IEEE, 2012, <10.1109/ICASSP.2012.6289144>
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Submitted on : Thursday, January 19, 2012 - 9:18:35 PM
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Mehrdad Yaghoobi, Sangnam Nam, Rémi Gribonval, Michael Davies. Noise Aware Analysis Operator Learning For Approximately Cosparse Signals . ICASSP - IEEE International Conference on Acoustics, Speech, and Signal Processing - 2012, Mar 2012, Kyoto, Japan. IEEE, 2012, <10.1109/ICASSP.2012.6289144>. <hal-00661549>

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