Application of diametrical clustering to tree-based matching pursuit for sinusoidal modeling

This paper deals with the application of Diametrical Clustering to the design of structured dictionaries in order to reduce the computational complexity of the Matching Pursuit algorithm for sinusoidal modeling. Diametrical Clustering organizes the dictionary in clusters, so that the similarity measure (average squared correlation coefficient between two atoms) is maximized. The optimal centroids are the dominant right singular vectors of the average correlation matrix of the atoms in the cluster. Some experiments are presented which show the suitability of this clustering algorithm, because the correlations of the atoms in a cluster with its centroid are much higher than the correlations with the centroids of other cluster. A dictionary of sinusoids has been divided in four clusters, and the centroids have been obtained and represented.