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With the evolution of smart cities, images are used in a wide range of services such as smart healthcare and surveillance. How to ensure that images are transmitted and shared securely is of paramount importance for smart cities. To this end, a secure and efficient scheme for image transmission is proposed in this paper, which uses sparse signal transformation (SST) and parallel compressive sensing (CS). The primary employed techniques are sparse signal transformation (SST), parallel CS, and diffusion-permutation operation. The compression performance is achieved by parallel CS, whereas the encryption performance is derived from SST, parallel CS, and diffusion-permutation procedure. SST is exploited to change energy information before CS sampling and incorporated into diffusion-permutation framework, which not only balances the security and the efficiency of the algorithm, but also improves the transmission efficiency of the cipher image. We introduce chaotic system to generate the measurement matrix, SST matrix, and diffusion matrix to improve security. Furthermore, numerical simulation results and theoretical analyses confirm the security performances and effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]