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, cipher-image coding by using compressed sensing (CS) has became a hot topic. However, the ratio-distortion (R-D) performance of the previous methods are barely satisfactory. In order to address this concern, a 2D CS (2DCS) scheme by using nonlocal low-rank prior (NLP) reconstruction is proposed in this letter. Firstly, the scrambling encryption is applied to mask the plaintext image. Secondly, the cipher image is compressed by 2DCS. Lastly, an iterative singular value thresholding (ISVT) algorithm is developed, which can reconstruct the image effectively by exploring the NLP information of the image. Simulation results show that the proposed method outperforms the previous CS-based methods in terms of 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.

In many practical scenarios, image encryption should be implemented before image compression. This leads to the requirement of compressing encrypted images. Compressed sensing (CS), a breakthrough in signal processing, has been demonstrated to be an effective method for compressing encrypted images with robustness. However, for the exiting CS-based image encryption-then-compression (ETC) systems, image encryption is usually performed by using linear operations. When linear operations are used, we cannot achieve low computational complexity and high security in the meantime. To solve this problem, a novel 2D CS (2DCS) based ETC (2DCS-ETC) scheme is proposed in this paper. First, two nonlinear operations, including global random permutation (GRP) and negative-positive transformation (NPT), are utilized to encrypt the original image for high security purpose. Second, the encrypted image is compressed by using 2DCS for low computational complexity purpose. Furthermore, a gray mapping operation is embedded prior to CS encoding. Since gray mapping strategy can reduce the dynamic range of the CS samples, this strategy is also helpful for the rate distortion (R-D) performance improvement. Third, a 2D projected gradient with embedding decryption (2DPG-ED) algorithm is proposed, which can be utilized for the original image reconstruction even if the encrypted image is not sparse anymore. Compared with the previous CS-based ETC methods, the proposed approach can simultaneously achieve high security and low computational complexity with better robustness.

Block compressed sensing (BCS) has great potential in image coding application for its low storage requirement and low computational complexity. However, in order to improve the reconstructed-image quality by eliminating block effect, joint reconstruction is used in the existing BCS algorithms. Thus, the computational complexity of those algorithms at decoder side is still high. To achieve a low complexity at both encoder and decoder sides while simultaneously improve the reconstructed-image quality, a novel BCS strategy with matrix permutation is introduced and investigated, in which matrix permutation is used prior to sampling to reduce the maximum block sparsity level of the 2D signal. Simulation results show that the novel matrix-permutation-based BCS approach gets a significant gain of peak signal-to-noise ratio (PSNR) of the reconstructed-images compared with the existing BCS approaches.