Matching pursuits with undercomplete dictionary

Matching pursuit (MP) is an iterative algorithm for signal representation which is applied widely to compression, feature extraction, signal denoising, and more. During last decades, main attention about the algorithm has been focused on the signal decomposition with respect to a complete or overcomplete dictionary. However, in this paper, we extend results by Mallat and Zhang about MP with overcomplete dictionaries to undercomplete one, and consider MP with a undercomplete dictionary. We investigate theoretically properties of undercomplete dictionary and demonstrate its binary partition ability to signal space. Furthermore, we derive bounds on the residual energy of any signal by MP with a undercomplete dictionary. Numerical simulations based on synthetic data are provided. Results show a promising pattern classification ability held by the MP with a undercomplete dictionary..