In intelligent transportation system, unprotected bare data transmission faces serious security threats and challenges. To this end, this paper proposes a visually secure traffic image encryption algorithm that combines a newly designed two-dimensional Sigmoid-type memristive chaotic map (2D-SMCM) with two-dimensional compressive sensing (2D-CS) and Laguerre transform (LT) embedding to provide services for secure transmission of private images. Specifically, first, the 2D-SMCM is used to generate pseudo-random sequences for subsequent compression, encryption and hiding operations. Second, the 2D-CS is utilized to compress the plain image to reduce the amount of data transmission. Then, encryption is completed by modifying the data values and their positions through index permutation and bidirectional diffusion. Finally, the encrypted data is embedded in the LT-processed public carrier medium for covert transmission. Experiments and performance analysis illustrate that the proposed scheme has good security, imperceptibility and reconstruction performance, with the average PSNRs of the cipher images and decrypted secret images up to 45.90 dB and 34.85 dB, respectively, using 500 grayscale images from the database BOWS2.