基于峰值变换的信号稀疏表示及重建

岑翼刚; 岑丽辉

doi:10.3724/SP.J.1146.2010.00305

基于峰值变换的信号稀疏表示及重建

doi: 10.3724/SP.J.1146.2010.00305

岑翼刚^{*① 岑丽辉,},
岑丽辉

基金项目:

国家自然科学基金(60802045, 60903066)，教育部留学回国人员基金([2009] 1001)，中央高校基本科研业务费(2009JBM028)和北京市自然科学基金(4102049)资助课题

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出版历程
- 收稿日期: 2010-03-26
- 修回日期: 2010-06-29
- 刊出日期: 2011-02-19

Sparse Representation and Reconstruction of Signals Based on the Peak Transform

Cen Yi-Gang^{*① 岑丽辉
,},
Cen Li-Hui

摘要

摘要: 压缩感知(CS)近年来的出现引起了学术界的极大关注，其要求信号本身是稀疏的或者在某种正交基下可以稀疏的表示。该文针对信号本身及小波变换下均不稀疏的情况(如线调频信号)，结合峰值变换(PT)，提出了PTCS的信号压缩感知算法，对于PT变换产生的峰值变换点序列采用可逆数字水印中的数值扩展方法，将峰值变换点序列嵌入测量信号中，避免了由于引入PT变换而额外增加测量点。通过PT变换，可以将不稀疏的小波系数变为稀疏系数，从而大大提升信号重构效果。仿真结果表明，该文提出的PTCS算法恢复信号与已有的基于正交匹配追踪算法的CS算法相比较，恢复信号质量有着较大的提高。
- 压缩感知 /
- 稀疏表示 /
- 峰值变换 /
- 小波变换 /
- 数值扩展
Abstract: The appearance of Compressed Sensing (CS) has been paid a great deal of attention over the world in the recent years. A basic requirement of CS is that a signal should be sparse or it can be sparsely represented in some orthogonal bases. Based on the Peak Transform (PT), a new algorithm called PTCS algorithm is proposed for the signals (such as the Linear Frequency Modulated signal) that are non-sparse themselves and can not be sparsely represented by wavelet transform. For the peak sequence produced by the Peak Transform, value expansion approach of reversible watermarking is exploited such that the peak sequence can be embedded into the measurements of the signal, which avoids increasing additional points for the transmission. By using the Peak Transform, non-sparse wavelet coefficients can be transformed into sparse coefficients, which greatly improves the reconstruction result of CS. Comparing with the original CS algorithm, simulation results show that the reconstruction results of the proposed PTCS algorithm significantly improves the reconstruction quality of signals.
- Compressed Sensing (CS) /
- Sparse representation /
- Peak Transform (PT) /
- Wavelet transform /
- Value expansion

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参考文献(1)

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