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Decreasing the correlation among the columns of the measurement matrix constitutes a significant technique for enhancing the quality of image reconstruction within the domain of compressed sensing. This paper introduces a novel one-dimensional homogenized composite mapping (1D-CICM) designed to generate chaotic measurement matrices for use in the compressed sensing process. The evaluation of information entropy, Lyapunov exponent, spectral entropy, and NIST SP800-22 test suggests that time series produced by the composite mapping possesses favorable non-periodic and uniform distribution characteristics, all while preserving its inherent chaotic attributes. The paper performed a correlation analysis on the measurement matrix constructed from time series produced by the composite mapping. The analysis shows that the columns of this measurement matrix have lower correlation among themselves. Further, the paper continues to construct an image compression-aware encryption algorithm centered on the 1D-CICM. By analyzing and evaluating PSNR, ciphertext pixel histogram, correlation, information entropy, and anti-differential attack test, the result analysis shows that the algorithm not only effectively improves the quality of reconstructed images at low compression ratios, but also improves the overall security of the encryption algorithm and its capability to withstand attacks.
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