视觉传感网中基于二次规划的图像压缩感知

为降低视觉传感网络中图像压缩感知算法的计算复杂度,提出一种基于二次规划的网络图像恢复算法。该算法将压缩感知重构中的欠定线性方程组求解问题,转化为有界约束二次规划问题,在此基础上结合阿米霍步长准则,设计一种压缩感知图像恢复算法,通过求解二次规划问题对网络图像数据进行恢复。理论分析和仿真结果表明,与传统图像压缩感知算法相比,该算法可减少约1/3的图像数据恢复运算时间,且图像重构质量提高3 dB~6 dB,有效提高了视觉传感器网络图像恢复算法的实时性。     

A first-order multigrid method for bound-constrained convex optimization

The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only consider bound constraints with (possibly) a single equality constraint. As our aim is to target large-scale problems, we want to avoid computation of second derivatives of the objective function, thus excluding Newton-like methods. We propose a smoothing operator that only uses first-order information and study the computational efficiency of the resulting method.     

On affine-scaling inexact dogleg methods for bound-constrained nonlinear systems

Within the framework of affine-scaling trust-region methods for bound-constrained problems, we discuss the use of an inexact dogleg method as a tool for simultaneously handling the trust-region and the bound constraints while seeking for an approximate minimizer of the model. Then, we focus on large-scale bound-constrained systems of nonlinear equations which often arise in practical applications when some of the unknowns are naturally subject to constraints due to physical arguments. We introduce an inexact affine-scaling method for such a class of problems that employs the inexact dogleg procedure. Global convergence results are established without any Lipschitz assumption on the Jacobian matrix, and locally fast convergence is shown under standard assumptions. Convergence analysis is performed without specifying the scaling matrix that is used to handle the bounds, and a rather general class of scaling matrices is allowed in actual algorithms. Numerical results showing the performance of the method are also given.