Recovery Error Analysis of Noisy Measurement in Compressed Sensing

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• 作者：Bin Wang ; Liaolin Hu ; Jingyu An ; Guangfei Liu…
• 关键词：Compressed sensing ; Recovery error bound ; Probabilistically bounded noise ; Probabilistically unbounded noise ; Restricted isometric property
• 刊名：Circuits, Systems, and Signal Processing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：36
• 期：1
• 页码：137-155
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Circuits and Systems; Electrical Engineering; Signal,Image and Speech Processing; Electronics and Microelectronics, Instrumentation;
• 出版者：Springer US
• ISSN：1531-5878
• 卷排序：36

文摘

With the rapid development of compressed sensing, practical consideration such as the impact of noise in the measurement should be considered. Existing methods for establishing recovery error bound suffer from inherent drawbacks and are only valid for specific types of noise. In this paper, we establish recovery error bound for various types of noise based on restricted isometric property. Our method is constructed from probability perspective. First, we establish the recovery error bound for noiseless signal to lay the foundation for further analysis. Depending on the probabilistic characteristics of different types of noise, we then establish recovery error bound for probabilistically bounded noise as well as for probabilistically unbounded noise. To further enhance the tightness of the bound, we also establish recovery error bound based on Dantzig-selector.