This paper proposes a joint selective encryption and data hiding scheme based on compressed sensing (CS), with a focus to its application in secure imaging. Specifically, working with a semantic-secure stream cipher, we suggest to selectively encrypt the sign bits of the CS measurements during its quantization stage and insert the authentication information using a nonseparable histogram-shifting based data hiding scheme. The rationale behind the sign encryption is that CS measurements, when measured by random subspace projection, is random in nature and thus, from both theoretical and experimental points of view, the mean squared errors associated with authorized users and attackers are significant. Due to the indistinguishability of the output ciphertext and the nonlinearity of the CS decoder, it is robust, when comparing with the existing selective encryption system of multimedia data, against known error concealment attacks. When applied in imaging, we demonstrate that it could effectively degrade the visual quality level while saving the computation load by at least 90%. Moreover, we further show that a state-of-the-art data hiding system can be seamlessly incorporated into the sign encryption, thus allowing soft data authentication without heavy computation. The proposed scheme is expected to strengthen the security of applications in the field where both energy and privacy are the concerns, such as sensitive information protection for multimedia data in wireless sensor networks.