Data collection and sharing have a tremendous impact on technology, business and society. Correspondingly, it brings in significant privacy and communication concerns. To this end, we present a hierarchical privacy-preserving and communication-efficient compression scheme via compressed sensing (CS) to address these two issues. In the encoding stage, the
obfuscated sensitive regions and non-sensitive regions are compressed and encrypted simultaneously. Consequently, the semi-authorized users and authorized users are considered in the decoding stage. Additionally, the left annihilator matrices provide various kinds of recovery qualities for real-world requirements, which further achieves communication-efficient compression.