Joint quantization and diffusion for compressed sensing measurements of natural images

Recent research advances have revealed the computational secrecy of the compressed sensing (CS) paradigm. Perfect secrecy can also be achieved by normalizing the CS measurement vector. However, these findings are established on real-valued measurements while digital devices can only store the samples at a finite precision. Based on the distribution of measurements of natural images sensed by structurally random ensemble, a joint quantization and diffusion approach for the real-valued measurements is suggested. In this way, a nonlinear cryptographic diffusion is intrinsically imposed on the CS quantization process and the overall security level is thus enhanced. It is shown that the proposed scheme is able to resist known-plaintext attack while the original CS scheme without quantization cannot.