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In this article, a continuous-time complex-valued projection neural network (CCPNN) in a matrix state space is first proposed for a general complex-variable basis pursuit problem. The proposed CCPNN is proved to be stable in the sense of Lyapunov and to be globally convergent to the optimal solution under the condition that the sensing matrix is not row full rank. Furthermore, an improved discrete-time complex projection neural network (IDCPNN) is proposed by discretizing the CCPNN model. The proposed IDCPNN consists of a two-step stop strategy to reduce the calculational cost. The proposed IDCPNN is theoretically guaranteed to be global convergent to the optimal solution. Finally, the proposed IDCPNN is applied to the reconstruction of sparse signals based on compressed sensing. Computed results show that the proposed IDCPNN is superior to related complex-valued neural networks and conventional basis pursuit algorithms in terms of solution quality and computation time. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In recent years, matrix-valued optimization algorithms have been studied to enhance the computational performance of vector-valued optimization algorithms. This paper presents two matrix-type projection neural networks, continuous-time and discrete-time ones, for solving matrix-valued optimization problems. The proposed continuous-time neural network may be viewed as a significant extension to the vector-type double projection neural network. More importantly, the proposed discrete-time projection neural network is suitable for parallel implementation in terms of matrix state spaces. Under pseudo-monotonicity and Lipschitz continuous conditions, the proposed two matrix-type projection neural networks are guaranteed to be globally convergent to the optimal solution. Finally, the proposed matrix-type projection neural network is effectively applied to image restoration. Computed examples show that the two proposed matrix-type projection neural networks are much superior to the vector-type projection neural networks in terms of computation speed. [ABSTRACT FROM AUTHOR]

Summary: With the application of computed tomography (CT) technology to the clinic diagnosis and image‐guided surgeries, various CT image reconstruction algorithms were presented for enhancing CT image quality based on different dose acquisitions. For wide and effective uses, this paper is going to provide a comprehensive survey on representative CT image reconstruction algorithms, in the light of low‐dose and high‐dose acquisitions and algorithm performance, including their merits and limitations. The algorithm performance and complexity are discussed under Gaussian and Poisson noise environments, respectively. Finally, experimental results analyze the efficiency and performance of several popular CT image reconstruction algorithms in terms of computation time and accuracy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an \boldsymbol \ell 1 -norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms. [ABSTRACT FROM PUBLISHER]

This letter proposes a novel double regularization unmixing-based method for hyperspectral image (HSI) superresolution. The proposed cost function contains two data-fidelity terms, the endmember regularization term and the abundance regularization term. Since the double regularization unmixing terms are able to exploit the spatial structure information of endmember and abundance, respectively, the nonnegative factorization (spectral unmixing) error is minimized. As a result, the performance of the proposed HSI superresolution method can be enhanced in terms of noise suppression and the special structure information preservation of reconstruction images. Finally, the associated optimization problem is effectively solved by an alternating direction optimization algorithm. Simulation results illustrate that the proposed method has a better performance than the state-of-the-art methods in terms of both visual effectiveness and quality indices. [ABSTRACT FROM PUBLISHER]

In this paper, we propose two fast complex-valued optimization algorithms for solving complex quadratic programming problems: 1) with linear equality constraints and 2) with both an l1 -norm constraint and linear equality constraints. By using Brandwood’s analytic theory, we prove the convergence of the two proposed algorithms under mild assumptions. The two proposed algorithms significantly generalize the existing complex-valued optimization algorithms for solving complex quadratic programming problems with an l1 -norm constraint only and unconstrained complex quadratic programming problems, respectively. Numerical simulations are presented to show that the two proposed algorithms have a faster speed than conventional real-valued optimization algorithms. [ABSTRACT FROM PUBLISHER]

The reconstruction of Poissonian image is an active research area in recent years. This paper proposes a novel method for Poissonian hyperspectral image superresolution by fusing a low-spatial-resolution hyperspectral image and a low-spectral-resolution multispectral image. The fusion scheme is designed as an optimization problem, whose cost function consists of the two data-fidelity terms about Poisson distribution, the sparse representation term, and the nonlocal regularization term. The two data-fidelity terms can capture statistical information of Poisson noise. The sparse representation term is used for enhancing the quality of sparsity-based signal reconstruction, and the nonlocal regularization term exploits the spatial similarity of hyperspectral image. As a result, the hyperspectral image and multispectral image are well fused. Finally, the designed optimization problem is effectively solved by an alternating direction optimization algorithm. Simulation results illustrate that the proposed method has a better performance than several well-known methods both in terms of quality indexes and reconstruction visual effect. [ABSTRACT FROM PUBLISHER]

Recently, cooperative recurrent neural networks for solving three linearly constrained L1 estimation problems were developed and applied to linear signal and image models under non-Gaussian noise environments. For wide applications, this paper proposes a compact cooperative recurrent neural network (CRNN) for calculating general constrained L1 norm estimators. It is shown that the proposed CRNN converges globally to the constrained L1 norm estimator without any condition. The proposed CRNN includes three existing CRNNs as its special cases. Unlike the three existing CRNNs, the proposed CRNN is easily applied and can deal with the nonlinear elliptical sphere constraint. Moreover, when computing the general constrained L1 norm estimator, the proposed CRNN has a fast convergence speed due to low computational complexity. Simulation results confirm further the good performance of the proposed CRNN. [ABSTRACT FROM AUTHOR]

Constrained optimization problems arise in a wide variety of scientific and engineering applications. Since several single recurrent neural networks when applied to solve constrained optimization problems for real-time engineering applications have shown some limitations, cooperative recurrent neural network approaches have been developed to overcome drawbacks of these single recurrent neural networks. This paper surveys in details work on cooperative recurrent neural networks for solving constrained optimization problems and their engineering applications, and points out their standing models from viewpoint of both convergence to the optimal solution and model complexity. We provide examples and comparisons to shown advantages of these models in the given applications. [ABSTRACT FROM AUTHOR]

In this paper, we present a delayed neural net- work approach to solve linear projection equations. The Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network. Compared with the existing linear projection neural network, theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems. [ABSTRACT FROM AUTHOR]

The output trajectory convergence of an extended projection neural network was developed under the positive definiteness condition of the Jacobian matrix of nonlinear mapping. This note offers several new convergence results. The state trajectory convergence and the output trajectory convergence of the extended projection neural network are obtained under the positive semi definiteness condition of the Jacobian matrix. Comparison and illustrative examples demonstrate applied significance of these new results. [ABSTRACT FROM AUTHOR]

A new regression estimator viewed as the solution of a strictly convex quadratic programming problem is introduced in this paper. Two recurrent neural networks in continuous-time and discrete-time respectively are proposed to solve the quadratic programming problem in real time. The continuous-time neural network is shown to have a global stability, including the global asymptotic and exponential stability. The discrete-time neural network is shown to have a global convergence with a fixed step length. This fixed step length can be independent of the regression problem size by scaling a design parameter. Since the sizes of the proposed neural networks depend only on the constraints of the optimization problems, the proposed new regression estimator can obtained by two novel neural networks with lower implementation costs than the conventional methods. Our simulation results confirm that the proposed neural networks are effective in solving various kind of regression problems. [ABSTRACT FROM AUTHOR]

This paper proposes a primal-dual neural network with a one-layer structure for online resolution of constrained kinematic redundancy in robot motion control. Unlike the Lagrangian network, the proposed neural network can handle physical constraints, such as joint limits and joint velocity limits. Compared with the existing primal-dual neural network, the proposed neural network has a low complexity for implementation. Compared with the existing dual neural network, the proposed neural network has no computation of matrix inversion. More importantly, the proposed neural network is theoretically proved to have not only a finite time convergence, but also an exponential convergence rate without any additional assumption. Simulation results show that the proposed neural network has a faster convergence rate than the dual neural network in effectively tracking for the motion control of kinematically redundant manipulators. [ABSTRACT FROM AUTHOR]

Presents information on a study which examined the global exponential stability of recurrent neural networks for solving optimization and related problems. Methodology of the study; Results and discussion on the study; Conclusions.

Presents a study which provided an alternative for the design of globally convergent optimization neural networks. Advantage of the proposed method; Description of a continuous-time neural network by differential equations; Findings of the study.

Presents information on a study which featured continuous-time and discrete-time recurrent neural networks for solving linear inequality and equality systems. Problem formulation; Model descriptions; Discussion on digital realization.

Presents two recurrent neural networks, a continuous-time one and a discrete-time one, for solving the assignment problem, an archetypical combinatorial optimization problem having widespread applications. Information on primal-dual assignment networks; Details on the assignment problem; Impact of the assignment problem on engineering or military applications; Details on the primal and dual assignment problems.