In this paper, we propose a color image compression and encryption algorithm that combines compressed sensing, Sudoku matrix, and hyperchaotic map to ensure the security of image data and improve transmission and storage efficiency. Firstly, we design a novel two-dimensional sine-logistic coupled hyperchaotic map that exhibits a more continuous and broader chaotic range and more complex hyperchaotic behavior compared to some existing known chaotic maps. Secondly, to mitigate the impact of compression thresholds on image reconstruction quality, we employ multiple optimization strategies to impr...