Nonnegative Dictionary-Learning Algorithm Based on L1 Norm with the Sparse Analysis Model

  • Yujie Li The University of Aizu
  • Shuxue Ding The University of Aizu
  • Zhenni Li The University of Aizu
  • Wuhui Chen The University of Aizu
Keywords: nonnegative dictionary learning, sparse representation, ℓ1-norm, analysis model


Sparse representation has been proven to be a powerful tool for analysis and processing of signals and images. Most of existing methods for sparse representation are based on the synthesis model. This paper presents a method for dictionary learning and sparse representation with the so-called analysis model. Different from the synthesis sparse model, in this analysis model, the analysis dictionary multiplying the signal can lead to a sparse outcome. The analysis dictionary learning problem has received less attention with and only a few algorithms has been proposed recently. What is more, there have still been few investigations in the context of dictionary learning for nonnegative signal representation. So, in this paper we focus on the nonnegative dictionary learning for signal representation. We use ℓ1-norm as the sparsity measure to learn an analysis dictionary from signals in analysis sparse model. In addition, we adopt the Euclidean distance as the error measure in the formulation. Numerical experiments on recovery of analysis dictionary show that the proposed analysis dictionary learning algorithm performs well for nonnegative signal representation.


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