The construction of the measurement matrix is a crucial factor influencing the reconstruction performance of compressive sensing techniques. To address the high storage cost of random measurement matrices and the difficulty in satisfying the restricted isometric property （RIP） with deterministic matrices， an improved method for constructing measurement matrices based on chaotic mapping is proposed. This method combines the random Gaussian matrix with the deterministic matrix and chaotic sequences， taking full the advantages of a small number of measurements from random Gaussian matrices and the lower correlation provided by chaotic mappings. Simultaneously， an analysis is conducted on the phase space characteristics of chaotic sequences， the RIP properties of measurement matrices， and the computational complexity involved in constructing optimized measurement matrices. Finally， simulation experiments compare random Gaussian matrices， Toeplitz matrices， and existing composite matrices. The results show that the proposed optimized measurement matrices outperform the other three types of matrices in terms of relative error， success reconstruction probability， and signal-to-noise ratio for one-dimensional random signals. Additionally， these optimized measurement matrices also exhibit improvements in the reconstruction time complexity， peak signal-to-noise ratio， structural similarity index， and mean structural similarity index for two-dimensional images， indicating better reconstruction performance and significant practical value.