Learning of structured graph dictionaries

We propose a method for learning dictionaries towards sparse ap-proximation of signals defined on vertices of arbitrary graphs. Dic-tionaries are expected to describe effectively the main spatial and spectral components of the signals of interest, so that their structure is dependent on the graph information and its spectral representa-tion. We first show how operators can be defined for capturing dif-ferent spectral components of signals on graphs. We then propose a dictionary learning algorithm built on a sparse approximation step and a dictionary update function, which iteratively leads to adapting the structured dictionary to the class of target signals. Experimental results on synthetic and natural signals on graphs demonstrate the efficiency of the proposed algorithm both in terms of sparse approx-imation and support recovery performance. Index Terms — dictionary learning, signal processing on graphs, sparse approximations 1