Convergence results for a self-dual regularization of convex problems

We study a one-parameter regularization technique for convex optimization problems whose main feature is self-duality with respect to the Legendre–Fenchel conjugation. The self-dual technique, introduced by Goebel, can be defined for both convex and saddle functions. When applied to the latter, we show that if a saddle function has at least one saddle point, then the sequence of saddle points of the regularized saddle functions converges to the saddle point of minimal norm of the original one. For convex problems with inequality and state constraints, we apply the regularization directly on the objective and constraint functions, and show that, under suitable conditions, the associated Lagrangians of the regularized problem hypo/epi-converge to the original Lagrangian, and that the associated value functions also epi-converge to the original one. Finally, we find explicit conditions ensuring that the regularized sequence satisfies Slater's condition.     

基于二阶广义全变差的多帧图像超分辨率重建

图像超分辨率重建是图像处理领域的重要问题.本文将二阶广义全变差用于基于正则化的多帧图像超分辨率重建问题,构建了基于二阶广义全变差正则项的图像超分辨率模型.为了更好地保持重建图像的边缘和细节,采用图像空域自适应正则化参数,并针对该重建模型的非光滑性,给出了基于半二次正则化和交替方向法的求解算法.实验结果表明该模型和数值算法能够较好地提高图像的分辨率,同时可以较好地保持图像的细节信息.     

基于无噪后验错误矢量信号能量的变正则因子仿射投影算法

变正则因子技术是提高仿射投影自适应算法性能的重要方法之一.由于环境噪声的影响,现有的变正则因子自适应算法收敛速度较慢且稳态误差较大,各种测量、评估误差的存在进一步恶化了算法性能.为提高自适应算法的跟踪性能,本文在分析无噪先验错误矢量、无噪后验错误矢量和额外均方错误间关系的基础上,提出通过最小化无噪后验错误矢量信号能量来推导自适应变正则因子表达式的方法.在实践应用中,该方法利用了测量噪声的统计方差特性,并提出一种更加光滑且更加容易控制的指数缩放因子评估方法.系统辨识的仿真结果表明本文方法与传统的变正则因子方法以及变步长方法相比有更快的收敛速度与更低的稳态误差.     

高动态短时突发扩频信号的快速捕获

针对低信噪比和大多普勒频移环境下,短帧突发直接序列扩频通信系统要求在短时间内以很低虚警和漏警概率捕获信号这一难题,设计了仅使用独特码的短时突发扩频信号帧结构,在接收端将扩频码与独特码作为一个复合扩频码看待,提出了基于FFT的高动态突发信号捕获方法,可同时快速完成突发信号检测、扩频码捕获、频偏估计、帧同步检测和位定时捕获等任务。仿真结果表明:该算法能有效消除多普勒频移对短时突发扩频信号捕获性能的影响。     

自适应约束下的双边全变差正则化超分辨率重建

在经典的双边全变差( BTV)超分辨率重建中,加权系数和正则化参数的恒定性导致重建结果边缘保持能力受限。为此,提出了一种自适应约束的BTV正则化先验模型。算法首先定义了图像的局部邻域残差均值以区分当前像素属于平坦区域还是边缘区域;然后针对加权系数的不变性导致边缘削弱的问题,利用边缘方向和垂直边缘方向扩散性的不同,设计自适应权重矩阵;最后根据代价函数的极值问题推导出迭代公式,从而进行图像的超分辨率重建,重建过程中采用自适应的方法确定正则化参数,以便求得代价函数的全局最优解,提高了算法的鲁棒性。实验结果表明：与双三次线性插值法和经典BTV算法相比,该算法取得了更好的视觉效果和更高的峰值信噪比,更多地保留了图像的边缘细节信息。     

一种基于多传感器的红外图像正则化超分辨率算法

提出一种红外图像多传感器超分辨率重建算法。 算法存在两个关键点:一是有效利用两类图像的相关性;二是针对红外图像的特点利用其自 身信息 构造正则化模型。采用相位一致性算法提取可见光图像边缘,利用此边缘信息对正则化模型 加权,以 充分利用可见光和红外图像的相关性;将一阶梯度锐化算子引入总广义变分模型,构成针对 红外 图像特点的正则化模型;最后采用一阶主-对偶优化算法求得加权后模型的最优解。实验表 明,本文算法可获得边缘清晰的重建结果,并且有效抑制噪声,在主观视觉效果和客观评价 指标方面均优于其他算法。     

A new approach to constant term identities and Selberg-type integrals

Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation based method that is powerful enough to establish many such identities in a simple manner. The main consequence is the proof of a conjecture of Forrester related to the Calogero–Sutherland model. In fact we prove a more general theorem, which includes Aomoto's constant term identity at the same time. We also demonstrate the relevance of the method in additive combinatorics.     

Pseudo almost periodic dynamics of delay Nicholson's blowflies model with a linear harvesting term

In this paper, we investigate a class of delay Nicholson's blowflies model with a linear harvesting term, new criteria for the existence and convergence dynamics of positive pseudo almost periodic solutions are established by using the fixed point method and the properties of pseudo almost periodic function, together with constructing suitable Lyapunov functionals. The obtained results extend previously known results, and they also partially answer an open problem proposed by L. Berezansky et al. Finally, an example with simulation is presented to demonstrate the effectiveness of theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

The long‐term extreme price risk measure of portfolio in inventory financing: An application to dynamic impawn rate interval

Different from the short‐term risk measure for traditional financial assets (stocks, bonds, etc.), the key to illiquid inventory portfolio traded in the over‐the‐counter markets is to estimate the long‐term extreme price risk with time varying volatility. In this article, a new long‐term extreme price risk (value at risk and conditional value at risk) measure method for inventory portfolio and an application to dynamic impawn rate interval are proposed. To realize this, we first establish AutoRegressive Moving Average‐Exponential Generalized Autoregressive Conditional Heteroskedasticity‐Extreme Value Theory model and multivariatet‐Copula to depict the autocorrelation, fat tails, and volatility clustering of returns of inventories and the nonlinear dependence structure of inventories. Furthermore, we obtain the long‐term extreme price risk with time varying volatility via Monte Carlo simulation instead of square‐root‐of time rule. The results show that, first, benefits from risk diversification is significant; second, long‐term extreme price risk measure of inventory portfolio via Monte Carlo method outperforms the square‐root‐of time rule; the last is that the dynamic rate interval based on the long‐term price risk is superior to the crude rules of thumb in terms of reducing efficiency loss and improving risk coverage. In summary, this article provides a new quantitative framework for managing the risk of portfolio in inventory financing practice for banks constrained by risk limitation. © 2014 Wiley Periodicals, Inc. Complexity 20: 17–34, 2015