Learning of structured graph dictionaries

• Published in: 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 3373 - 3376
• Main Authors: Xuan Zhang, Xiaowen Dong, Frossard, P.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.03.2012
• Subjects: Approximation algorithms; Approximation error; Dictionaries; dictionary learning; Noise; signal processing on graphs; sparse approximations; Testing; Training
• ISBN: 1467300454; 9781467300452
• ISSN: 1520-6149; 2379-190X
• DOI: 10.1109/ICASSP.2012.6288639

We propose a method for learning dictionaries towards sparse approximation of signals defined on vertices of arbitrary graphs. Dictionaries 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 representation. We first show how operators can be defined for capturing different 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 approximation and support recovery performance.