A novel signal sparse decomposition based on modulation correlation partition

• An algorithm that raises efficiency of matching pursuit is proposed.
• Partition strategy is introduced to improve structure of redundant dictionary.
• The proposed approach is more effective than the traditional ones and has robustness.

The prohibitive computational complexity caused by redundant dictionary which is used in signal sparse decomposition has always been perplexing researchers of signal processing all the time. However, large over-complete dictionaries are essential to approximate the signal. In this paper, a decomposition algorithm based on modulation correlation partition (PBMC) is introduced, which improves the process of searching matched atoms in the redundant dictionary of functions. Through analyzing the structure of signals, we unite the frequency factor and phase factor to obtain the 2D modulation factor. The over-complete dictionary is partitioned into several sub-dictionaries according to the modulation correlation of atoms. Each sub-dictionary is represented by a single selected atom which is used in the greedy algorithm. At the end of this paper, experimental results show that the computational complexity of signal sparse decomposition can be adequately reduced by partitioning over-complete dictionary without impacting the decomposition result.