Construction And Performance Analysis Of Chatic Sparse Measurement Matrix

Compressed Sensing breaks the limitation of the traditional Nyquist sampling theory.Under certain conditions,the signal can be sampled at a much lower frequency than Nyquist sampling rate,and can have high probability of reconstruction.Research on construction of the measurement matrix in compressed sensing as follows,by utilizing the pseudo-random,ergodicity of the chaotic system and the uniform distribution of tent map,a method of constructing deterministic sparse random matrices based on chaotic sequences of tents is proposed.The theoretical and empirical experiments show that the constructed chaotic sparse measurement matrix satisfies the RIP properties.The simulation results show that the proposed method has the similar reconstruction performance with Gaussian random matrix,sparse random matrix and Bernoulli random matrix.The chaotic sparse measurement matrix is deterministic when chaos system parameters and initial value are fixed.Therefore,the construction method is computationally small and easy to implement.