Signal Sparse Representation Based on the Peak Transform and Modulus Maximum of Wavelet Coefficients

10.6180/jase.2011.14.3.05

Yi-Gang Cen；Rui Xin；Xiao-Fang Chen；Li-Hui Cen；Ming-Xing Hu；Shi-Ming Chen

Compressed Sensing ； Sparse Representation ； Peak Transform ； Modulus Maximum ； Wavelet Transform

淡江理工學刊

14卷3期（2011 / 09 / 01）

217 - 224

英文

It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements. This technique is known as ”compressed sensing” or ”compressive sampling” (CS). Abasic 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) and modulus maximum of wavelet coefficients, a new algorithm was proposed for the signals that are non-sparse themselves and can not be sparsely represented by wavelet transform such as the Linear Frequency Modulated signal. According to this algorithm, K-sparse wavelet coefficients can be obtained. 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 transmission. By using the Peak Transform and modulus maximum, non-sparse wavelet coefficients can be transformed into K-sparse coefficients, which improves the reconstruction result of CS. Simulation results showed that our proposed algorithm achieved better performance comparing with the original CS algorithm.

1. 范植翔(2016)。以Apache Spark框架設計OpenStack雲端系統日誌平行化分析叢集系統之研究。臺中科技大學資訊工程系碩士班學位論文。2016。1-100。