Matrix-variable optimization is a generalization of vector-variable optimization and has been found to have many important applications. To reduce computation time and storage requirement, this article presents two matrix-form recurrent neural networks (RNNs), one continuous-time model and another discrete-time model, for solving matrix-variable optimization problems with linear constraints. The two proposed matrix-form RNNs have low complexity and are suitable for parallel implementation in terms of matrix state space. The proposed continuous-time matrix-form RNN can significantly generalize existing continuous-time vector-form RNN. The proposed discrete-time matrix-form RNN can be effectively used in blind image restoration, where the storage requirement and computational cost are largely reduced. Theoretically, the two proposed matrix-form RNNs are guaranteed to be globally convergent to the optimal solution under mild conditions. Computed results show that the proposed matrix-form RNN-based algorithm is superior to related vector-form RNN and matrix-form RNN-based algorithms, in terms of computation time.

Because of the robustness and sparsity performance of least absolute deviation (LAD or$l_{1}$) optimization, developing effective solution methods becomes an important topic. Recurrent neural networks (RNNs) are reported to be capable of effectively solving constrained$l_{1}$-norm optimization problems, but their convergence speed is limited. To accelerate the convergence, this article introduces two RNNs, in form of continuous- and discrete-time systems, for solving$l_{1}$-norm optimization problems with linear equality and inequality constraints. The RNNs are theoretically proven to be globally convergent to optimal solutions without any condition. With reduced model complexity, the two RNNs can significantly expedite constrained$l_{1}$-norm optimization. Numerical simulation results show that the two RNNs spend much less computational time than related RNNs and numerical optimization algorithms for linearly constrained$l_{1}$-norm optimization.

Face antispoofing detection aims to identify whether the user’s face identity information is legal. Multimodality models generally have high accuracy. However, the existing works of face antispoofing detection have the problem of insufficient research on the safety of the model itself. Therefore, the purpose of this paper is to explore the vulnerability of existing face antispoofing models, especially multimodality models, when resisting various types of attacks. In this paper, we firstly study the resistance ability of multimodality models when they encounter white-box attacks and black-box attacks from the perspective of adversarial examples. Then, we propose a new method that combines mixed adversarial training and differentiable high-frequency suppression modules to effectively improve model safety. Experimental results show that the accuracy of the multimodality face antispoofing model is reduced from over 90% to about 10% when it is attacked by adversarial examples. But, after applying the proposed defence method, the model can still maintain more than 90% accuracy on original examples, and the accuracy of the model can reach more than 80% on attack examples.

Super resolution image reconstruction under unknown Gaussian blur has been a challenging topic. Advanced optimization-based works for blind image super-resolution (SR) were reported to be effective, but there exist both large data space storage and time consuming due to vector-variable optimization. This paper proposes a matrix-variable optimization method for fast blind image SR. We first present an accurate blur kernel estimation-based matrix decomposition method. Then we propose minimizing a matrix-variable optimization problem with sparse representation and TV regularization terms. The proposed method can exactly estimate the unknown blur kernel and blur matrix. Compared with vector-variable optimization based methods for blind image SR, the proposed method can greatly reduce their data space storage and computation time. Compared with deep learning methods, the proposed method can directly deal with multiframe SR problem without training and learning task. Experimental results show that the proposed algorithm is superior to conventional optimization-based method in terms of solution quality and computation time. Moreover, the proposed method can obtain higher reconstruction quality than the deep learning methods, specially in the case of large blur kernels.

Blind image deblurring has been a challenging issue due to the unknown blur and computation problem. Recently, the matrix-variable optimization method successfully demonstrates its potential advantages in computation. This paper proposes an effective matrix-variable optimization method for blind image deblurring. Blur kernel matrix is exactly decomposed by a direct SVD technique. The blur kernel and original image are well estimated by minimizing a matrix-variable optimization problem with blur kernel constraints. A matrix-type alternative iterative algorithm is proposed to solve the matrix-variable optimization problem. Finally, experimental results show that the proposed blind image deblurring method is much superior to the state-of-the-art blind image deblurring algorithms in terms of image quality and computation time.