Dual Adaptive K-SVD Algorithm Based on a Rank Symmetrical Relationship

Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. The K-SVD algorithm is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. However, the existing K-SVD algorithm is employed to a single feature space meaning that the pursuit algorithms are assigned to the given subspace definitely. The work proposed in this paper provides a novel adaptive way to adapting dictionaries in order to achieve the dual subspace sparse signal representations, the update of the dictionary is combined with a rank symmetrical relationship of the proposed dual subspace by incorporated a new mechanism of matrix transform, which is called dual K-SVD. Experimental results conducted on the ORL and Yale face databases demonstrate the effectiveness of the proposed method.