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.

Compressed sensing (CS), a popular signal processing technique, can achieve compression and encryption simultaneously. Therefore, it has extension applications in various fields. However, CS is vulnerable to cryptographic attacks for its linear encoding process. To solve this problem, a permutation-diffusion structure is designed and embedded to the CS encoding process. In addition, it can increase the key space while compressing. Since the permutation-diffusion structure reduces the sparseness, superior recovery performance cannot be achieved. Therefore, the multi-prior regularization recovery strategy is designed to improve the recovery performance, where the multi-prior regularization term denotes l1 norm, total variation (TV) and low rank. The simulation results and analyses demonstrate that the proposed encoding scheme can resist cryptographic attacks, increase the key space while compressing, and achieve 1.54dB PSNR gain on average in comparison with the existing schemes.

As a new signal processing technology, compressed sensing (CS) has been showed to be a promising solution for compressing cipher images. However, the previous CS-based schemes are unsatisfactory in terms of ratio-distortion (R-D) performance. In order to solve this problem, an image encryption-then-compression (ETC) scheme by using semi-tensor product CS (STP-CS) and pre-mapping is proposed in this paper. In the proposed scheme, the original image is encrypted by using the scrambling operation. After image encryption, the cipher image is compressed through three steps. Firstly, the original image is compressed by using STP-CS. Secondly, the CS samples are processed by using pre-mapping operation. Thirdly, the resultant CS samples are quantized and encoded into bits. For image signal recovery, an iterative bivariate shrinkage (IBS) algorithm is proposed. Compared with the existing CS-based image ETC schemes, the proposed scheme has better R-D performance.