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Ways to sparse representation:An overview

Science in China(Series F) 2009年第4期52卷 695-703页

作者： YANG JingYu PENG YiGang XU WenLi DAI QiongHai Department of Automation Tsinghua University Beijing 100084 China

Many algorithms have been proposed to find sparse representations over redundant dictionaries or transforms. This paper gives an overview of these algorithms by classifying them into three categories： greedy pursuit algorithms, lp norm regularization based algorithms, and iterative shrinkage algorithms. We summarize their pros and cons as well as their connections. Based on recent evidence, we conclude that the algorithms of the three categories share the same root： lp norm regularized inverse problem. Finally, several topics that deserve further investigation are also discussed.

关键词： sparse representation redundant dictionary redundant transform nonlinear approximation matching pursuit basis pursuit iterativeshrinkage

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Sparse Decomposition Algorithm Using Immune Matching Pursuit

Sparse Decomposition Algorithm Using Immune Matching Pursuit

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2012 IEEE 11th International Conference on Signal Processing(ICSP 2012)

作者： Yan Zhou Heming Zhao Tao Liu School of Electronics and Information Engineering Soochow University Department of Electronics and Information Engineering Soochow Vocational University

The optimal sparse expression for a signal is critical to the application of compressed sensing theory. Since the standard matching pursuit uses greedy strategy to approximate the objective function, which is aim to search for the linear combination of the optimal atoms in a redundant dictionary. It is inevitable to cause enormous calculation quantity, to overcome this defect, a scheme based on immune matching pursuit algorithm is proposed in this paper which is suitable for speech signal sparse decomposition. In this matching pursuit algorithm, each matching process has been optimized by the immune algorithm with the characteristics of local fast convergence and global optimal. As a result, according to this algorithm, the speed of sparse decomposition and the quality of reconstructed signal all have been effectively improved, and the storage space requirement for redundant dictionary also has been degraded. Simulation results show that, the matching pursuit computational cost can be obviously reduced by using this algorithm, Moreover, the performance of this algorithm is stable, and it also has high signal decomposition accuracy. In a word, the efficiency of sparse decomposition can be significantly improved by combining the immune evolution mechanism and matching pursuit algorithm.

关键词： Matching Pursuit Immune Algorithm Sparse decomposition redundant dictionary Reconstructed signal

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