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Aiming at the problems that common chaotic mapping has low randomness, sequence elements has strong correlation, and constructing the measurement matrix elements requires interval sampling to satisfy the independence of data statistics, a new composite chaotic system is constructed by cascading quantum Logistic chaotic system and generalized Fibonacci sequence. In terms of information entropy, spatial characteristics and correlation coefficients, different chaotic measurement matrices are quantitatively analyzed to verify that the proposed chaotic system has ergodicity and high chaos. Moreover, the sequence elements have low correlation, which satisfies the independence of data statistics. At the same time, it is proved that the compressed sensing measurement matrix constructed by the proposed chaotic system satisfies the RIP condition. Simulation and discussion on one-dimensional sparse signal and two-dimensional image show that, compared with other measurement matrices, when the sampling rate is 1/2, the proposal increases the success rate of reconstructing one-dimensional sparse signals by 4 %, and increases the SNR rate of reconstructing two-dimensional images by 0. 2dB. It improves the data utilization rate and overcomes the great waste of data resources caused by the interval sampling of other chaotic measurement matrices. [ABSTRACT FROM AUTHOR]