Compressed sensing (CS) has attracted wide attention in signal process field, which states that a sparse signal or a compressive signal can be reconstructed by using a small number of CS samples efficiently. In recent years, CS-based image coding methods have been investigated extensively. However, the ratio-distortion (R-D) performance of this method is unsatisfactory in comparison with traditional compression algorithms, such as JPEG and JPEG2000.

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.

In recent years, using compressed sensing (CS) as a cryptosystem has drawn more and more attention since this cryptosystem can perform compression and encryption simultaneously. However, this cryptosystem is vulnerable to known-plaintext attack (KPA) under multi-time-sampling (MTS) scenario due to the linearity of its encoding process. In this paper, a privacy-preserving CS scheme for image compression-encryption applications is proposed, which embeds a non-linear operation called noise injected negative-positive transformation (NINPT) in the CS encoding process with the purpose of withstanding KPA. The encoding procedures of the proposed scheme include three steps. First, the original image is encrypted by using NINPT operation. Second, the intermediate ciphertext is re-encrypted and compressed by using CS simultaneously. Third, the final compressed ciphertext is quantized into bits via scalar quantization (SQ). Since the introduction of NINPT operation in the CS encoding process breaks the linearity of the CS sampling process, the proposed scheme can withstand KPA under MTS scenario. For image signal reconstruction, a projected Landweber with embedding decryption (PL-ED) algorithm is proposed. Simulation results demonstrate that the proposed scheme can withstand KPA under MTS scenario at the cost of slightly sacrificing the compression performance.