Noise Aware Analysis Operator Learning For Approximately Cosparse Signals

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.
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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. ⟨10.1109/ICASSP.2012.6289144⟩. ⟨hal-00661549⟩

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