Abstract
ABSTRACTIn this paper, we propose a high efficiency deterministic measurement matrix for practical compressive sensing based on the combination of Logistic Chaotic system and correlation, called Chaos-Gaussian measurement matrix. Initially, deterministic Logistic system has been used to generate Chaotic sequence with good pseudo-random. Subsequently, two spread spectrum sequences have been constructed and been verified to follow Gaussian distribution. On the basis of the observation mentioned previously, Chaos-Gaussian measurement matrix is constructed. Experimental results corroborate that Chaos-Gaussian measurement matrix is superior to Gaussian and Bernoulli random measurement matrix. Furthermore, Chaos-Gaussian measurement matrix balances the randomness and the certainty.
Highlights
In the information field, the traditional informationcapturing paradigm always follows the well-known Shannon-Nyquist sampling theory (Ponuma & Amutha, 2017), which states that the signal sampling rate reaches more than twice the signal bandwidth
We propose a high efficiency deterministic measurement matrix for practical compressive sensing based on the combination of Logistic Chaotic system and correlation, called ChaosGaussian measurement matrix
For the sake of visual observation, we take the peppers image as an example, and the reconstruction performance of different measurement matrices is discussed under the compression ratio M/N = 0.5
Summary
The traditional informationcapturing paradigm always follows the well-known Shannon-Nyquist sampling theory (Ponuma & Amutha, 2017), which states that the signal sampling rate reaches more than twice the signal bandwidth. This paradigm increases the storage consumption and transmission bandwidth. The reconstruction performance of these matrices is good, but the uncertainty of the random measurement matrix increases the computational complexity. Thereafter, a measurement matrix is proposed on the basis of the deterministic random sequence obtained using the chaotic sequence in (Wang, Li, & Shen, 2013).
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