﻿ 基于噪声特性分析的稀疏度估计方法

# 基于噪声特性分析的稀疏度估计方法Sparsity Estimation Method Based on Noise Characteristic Analysis

Abstract: The sparse representation, after decades of development, has been deeply studied and applied in many fields. Estimation of signal sparsity is an important part of the work in the sparse decomposition of signal. According to the noise characteristics, this paper proposes a method for estimating sparse degree. By constructing the Fourier base dictionary, using the uniform distribution characteristics of noise energy in the whole frequency domain, and through the sparse characteristics of signal traversing the full spectrum, the accuracy of the signal sparsity is gradually determined. Simulation results show that the proposed method can effectively complete the estimation of signal sparsity.

[1] 马原, 吕群波, 刘扬阳, 钱路路, 裴琳琳. 基于主成分变换的图像稀疏度估计方法[J]. 物理学报, 2013, 62(20): 204-202.

[2] Kim, E. and Paul, G. (1987) Principal Component Analysis. Elsevier Science Publishers, Amsterdam, 37-52.

[3] Meyer, Y. (1993) Wavelets and Operators. Cambridge University Press, Cambridge.

[4] 张鹏飞, 金晓康, 汤倩, 张建明. 学习字典下自适应稀疏度估计的分解去噪算法[J]. 福建电脑, 2015(1): 6-8.

[5] 徐勇俊. 基于信号稀疏表示的字典设计[D]: [硕士学位论文]. 南京: 南京理工大学, 2013.

[6] 郭俊锋, 郑晓慧, 魏兴春. 滚动轴承振动信号的稀疏表示研究[J]. 甘肃科学学报, 2014, 26(3): 91-94.

[7] 彭志珍. 基于改进的匹配追踪算法的信号稀疏分解[D]: [硕士学位论文]. 武汉: 华中科技大学, 2011.

[8] 沈益青. 匹配追踪算法中稀疏度的自适应研究[D]: [硕士学位论文]. 杭州: 浙江大学, 2013.

[9] Traub, J.F. and Woziakowski, H. (1980) A General Theory of Optimal Algorithms. Academic, New York.

[10] Donoho, D.L., Elad, M. and Temlyakov, V. (2006) Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise. IEEE Transactions on Information Theory, 52, 6-18.

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