一种引入退火降温阈值函数约束的改进MP稀疏分解方法

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基金项目:

教育部科学技术研究重点项目(02065), 高等学校博士学科点专项科研基金, 教育部青年教师奖励计划资助课题

A modified MP Algorithm Constrained by the Simulate Annealing Threshold for Sparse Decomposition of Signals

摘要: 匹配追踪(Matching pursuit, MP)方法可以在过完备库中实现信号的稀疏、能量集中的分解。该文从对信号分解稀疏性的有利原则出发，在迭代过程中，将过完备库划分为新(未选择过的)、旧(已选择过的)原子库，通过引入退火降温阈值函数来约束迭代过程中最优原子的选择，使选择的最优原子比原始MP方法有更大的可能性落入对信号稀疏性有利的旧原子库中，从而实现对信号更加稀疏的分解。对余弦调制指数信号和一段语音信号的分解结果，证实了改进MP方法对信号有更加稀疏的分解结果。
- 信号处理;稀疏性;匹配追踪;退火函数
Abstract: Signal can be decomposed sparsely and power-focally in an over-complete dictionary with Matching Pursuit (MP). This paper proposes a modified MP method to decompose signal more sparsely. In the iteration procedure of the modified MP, the over-complete dictionary is classified into two separate dictionaries with the selected and unselected atoms, the algorithm is designed to have more chances than the original MP to choose the atom in the selected atom dictionary as the optimal atom by a simulate annealing threshold function, thus the algorithm availed for a more sparse decomposition. The decomposition results for a cosine-modulated exponential signal and an actual speech signal show that the proposed modified MP can decompose signal more sparsely.