Balancing spectral, spatial, and temporal resolutions is a key challenge in spectral imaging. The Dual-Camera Coded Aperture Snapshot Spectral Imaging (DC-CASSI) system alleviates this trade-off but suffers from severely ill-posed reconstruction problems due to its high compression ratio. Existing methods are constrained by scene-specific tuning or excessive reliance on paired training data. To address these issues, we propose a Total Variation (TV) subgradient-guided multi-source fusion framework for DC-CASSI reconstruction, comprising three core components: (1) An end-to-end Single-Disperser CASSI (SD-CASSI) observation model based on the tensor-form Kronecker δ, which establishes a rigorous mathematical foundation for physical constraints while enabling efficient adjoint operator implementation; (2) An adaptive spatial reference generator that integrates SD-CASSI’s physical model and RGB subspace constraint, generating the reference image as reliable spatial prior; (3) A TV subgradient-guided regularization term that encodes local structural directions from the reference image into spectral reconstruction, achieving high-quality fused results. The framework is validated on simulated datasets and real-world datasets. Experimental results demonstrate that it achieves state-of-the-art reconstruction performance and robust noise resilience. This work not only establishes an interpretable theoretical foundation for subgradient-guided fusion but also provides a practical fusion-based paradigm for high-fidelity spectral image reconstruction in DC-CASSI systems. Source code: https://github.com/bestwishes43/ADMM-TVDS.

Matching is an important prerequisite for point clouds registration, which is to establish a reliable correspondence between two point clouds. This paper aims to improve recent theoretical and algorithmic results on discrete optimal transport (DOT), since it lacks robustness for the point clouds matching problems with large-scale affine or even nonlinear transformation. We first consider the importance of the used prior probability for accurate matching and give some theoretical analysis. Then, to solve the point clouds matching problems with complex deformation and noise, we propose an improved DOT model, which introduces an orthogonal matrix and a diagonal matrix into the classical DOT model. To enhance its capability of dealing with cases with outliers, we further bring forward a relaxed and regularized DOT model. Meantime, we propose two algorithms to solve the brought forward two models. Finally, extensive experiments on some real datasets are designed in the presence of reflection, large-scale rotation, stretch, noise, and outliers. Some state-of-the-art methods, including CPD, APM, RANSAC, TPS-ICP, TPS-RPM, RPMNet, and classical DOT methods, are to be discussed and compared. For different levels of degradation, the numerical results demonstrate that the proposed methods perform more favorably and robustly than the other methods.

This paper considers a class of distributed convex optimization problems with constraints and gives a novel multiagent neurodynamic approach in continuous-time form. The considered distributed optimization is to search for a minimizer of the summation of nonsmooth convex functions on some agents, which have local general constraints. The proposed approach solves the objective function of each agent individually, and the state solutions of all agents reach consensus asymptotically under mild assumptions. In particular, the existence and boundedness of the global state solution to the dynamical system are guaranteed. Moreover, the state solution reaches the feasible region of equivalent optimization problem asymptotically and the output of each agent is convergent to the optimal solution set of the primal distributed problem. In contrast to the existing methods in a distributed manner, the proposed approach is more convenient for general constrained distributed problems and has low structure complexity which could narrow the bandwidth of communication. Finally, the proposed neurodynamic approach is applied to two numerical examples and a class of power system optimal load-sharing problems to support the theoretical results and its efficiency.

In this article, we consider a class of nonsmooth, nonconvex, and non-Lipschitz optimization problems, which have wide applications in sparse optimization. We generalize the Clarke stationary point and define a kind of generalized stationary point of the problems with a stronger optimal capability. Based on the smoothing method, we propose a projected neural network for solving this kind of optimization problem. Under the condition that the level set of objective function in the feasible region is bounded, we prove that the solution of the proposed neural network is globally existent and bounded. The uniqueness of the solution of the proposed network is also analyzed. When the feasible region is bounded, any accumulation point of the proposed neural network is a generalized stationary point of the optimization model. Based on some suitable conditions, any solution of the proposed neural network is asymptotic convergent to one stationary point. In particular, we give some deep analysis on the proposed network for solving a special class of the non-Lipschitz optimization problem, which indicates a lower bound property and the unify identification for the nonzero elements of all accumulation points. Finally, some numerical results are presented to show the efficiency of the proposed neural network for solving some kinds of sparse optimization models.

Nonsmooth nonconvex optimization models have been widely used in the restoration and reconstruction of real images. In this paper, we consider a linearly constrained optimization problem with a non-Lipschitz regularization term in the objective function which includes the $l_p$ norm ($0

A neural network based on smoothing approximation is presented for a class of nonsmooth, nonconvex constrained optimization problems, where the objective function is nonsmooth and nonconvex, the equality constraint functions are linear and the inequality constraint functions are nonsmooth, convex. This approach can find a Clarke stationary point of the optimization problem by following a continuous path defined by a solution of an ordinary differential equation. The global convergence is guaranteed if either the feasible set is bounded or the objective function is level bounded. Specially, the proposed network does not require: 1) the initial point to be feasible; 2) a prior penalty parameter to be chosen exactly; 3) a differential inclusion to be solved. Numerical experiments and comparisons with some existing algorithms are presented to illustrate the theoretical results and show the efficiency of the proposed network.

In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of . Using the smoothing approximate techniques, the proposed neural network is modeled by a differential equation, which can be implemented easily. Under the level bounded condition on the objective function in the feasible set, we prove the global existence and uniform boundedness of the solutions of the SNN with any initial point in the feasible set. The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing functions. We show that any accumulation point of the solutions of the SNN is a stationary point of the optimization problem. Numerical results including image restoration, blind source separation, variable selection, and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the SNN. Comparisons with some existing algorithms show the advantages of the SNN.

This paper presents a subgradient-based neural network to solve a nonsmooth nonconvex optimization problem with a nonsmooth nonconvex objective function, a class of affine equality constraints, and a class of nonsmooth convex inequality constraints. The proposed neural network is modeled with a differential inclusion. Under a suitable assumption on the constraint set and a proper assumption on the objective function, it is proved that for a sufficiently large penalty parameter, there exists a unique global solution to the neural network and the trajectory of the network can reach the feasible region in finite time and stay there thereafter. It is proved that the trajectory of the neural network converges to the set which consists of the equilibrium points of the neural network, and coincides with the set which consists of the critical points of the objective function in the feasible region. A condition is given to ensure the convergence to the equilibrium point set in finite time. Moreover, under suitable assumptions, the coincidence between the solution to the differential inclusion and the "slow solution" of it is also proved. Furthermore, three typical examples are given to present the effectiveness of the theoretic results obtained in this paper and the good performance of the proposed neural network.