Abstract
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.
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