Recently, to conquer most non-plain related chaos-based image cryptosystems’ security flaws that cannot resist the powerful chosen/knownn plain-text attacks or differential attacks efficiently for less plaintext sensitivity, many plain related chaos-based image cryptosystems have been developed. Most cryptosystems that have adopted the traditional permutation–diffusion structure still have some drawbacks and security flaws: (1) most plaintext related image encryption schemes using only plaintext related confusion operation or only plaintext related diffusion operation relate to plaintext inadequately that cannot achieve high plaintext sensitivity; (2) in some algorithms, the generation of security key that needs to be sent to the receiver is determined by the original image, so these algorithms may not applicable to real-time image encryption; (3) most plaintext related image encryption schemes have less efficiency because more than one round permutation–diffusion operation is required to achieve high security. To obtain high security and efficiency, a simple chaotic based color image encryption system by using both plaintext related permutation and diffusion is presented in this paper. In our cryptosystem, the values of the parameters of cat map used in permutation stage are related to plain image and the parameters of cat map are also influenced by the diffusion operation. Thus, both the permutation stage and diffusion stage are related to plain images, which can obtain high key sensitivity and plaintext sensitivity to resist chosen/known plaintext attacks or differential attacks efficiently. Furthermore, only one round of plaintext related permutation and diffusion operation is performed to process the original image to obtain cipher image. Thus, the proposed scheme has high efficiency. Complete simulations are given and the simulation results prove the excellent security and efficiency of the proposed scheme.

Various image datasets appear naturally in the form of multi-dimensional arrays (hypermatrices), called tensors. Image with incomplete entries, which often can be formulated as the low-rank tensor completion problem, is practically important in order to process large size 3D array images both efficiently and effectively. To make the low-rank approximation being tractable, most current approaches make use of the lower convex envelope of tensor multi-rank function for the approximation. Due to the gap between the rank function and its lower convex envelope, the adoption of tensor nuclear norm may lead to the approximation of the corresponding tensor tubal-rank being insufficient. In this paper, we introduce a new nonconvex regularization approach, which can better capture the low-rank characteristics than the convex approach. By transforming the original problem to the Fourier domain, we formulate an equivalent optimization problem with more transparent tensor rank characteristics, whose explicit solution can be obtained under our framework. A minimization algorithm, associated with the augmented Lagrangian multipliers and the nonconvex regularizer, is established and is shown to be feasible. The constructed sequence converges to the desirable Karush-Kuhn-Tucker point, which is mathematically validated in detail. Extensive experimental results demonstrate that our proposed approach outperforms the existing state-of-the-art convex approaches consistently.

Tensor Robust Principal Component Analysis (TRPCA) plays a critical role in handling high multi-dimensional data sets, aiming to recover the low-rank and sparse components both accurately and efficiently. In this paper, different from current approach, we developed a new t-Gamma tensor quasi-norm as a non-convex regularization to approximate the low-rank component. Compared to various convex regularization, this new configuration not only can better capture the tensor rank but also provides a simplified approach. An optimization process is conducted via tensor singular decomposition and an efficient augmented Lagrange multiplier algorithm is established. Extensive experimental results demonstrate that our new approach outperforms current state-of-the-art algorithms in terms of accuracy and efficiency.

In this paper, we study the image multiview subspace clustering problem via a nonconvex low-rank representation under the framework of tensors. Most of the recent studies of tensor based multiview ...