Some First-Order Algorithms for Total Variation Based Image Restoration

This paper deals with first-order numerical schemes for image restoration. These schemes rely on a duality-based algorithm proposed in 1979 by Bermùdez and Moreno. This is an old and forgotten algorithm that is revealed wider than recent schemes (such as the Chambolle projection algorithm) and able to improve contemporary schemes. Total variation regularization and smoothed total variation regularization are investigated. Algorithms are presented for such regularizations in image restoration. We prove the convergence of all the proposed schemes. We illustrate our study with numerous numerical examples. We make some comparisons with a class of efficient algorithms (proved to be optimal among first-order numerical schemes) recently introduced by Y. Nesterov.     

无线传感器网络整合时钟同步方案

针对多数无线传感器网络时钟同步方案存在的仅纠正时钟偏移问题,提出一种新的解决方案,整合时钟偏移同步和时钟速率同步,通过3个连续的消息传输实现单跳同步,采用分层的生成树实现多跳同步。仿真实验结果表明,与现有的同步方案比较,该方案的同步错误更小,能够获得更长的再同步周期。     

微球探针制备工艺的优化

为了解决现有激光微球探针加工技术中存在的探针尖端微球球心偏离针杆中轴线的问题,提出了一个两步法加工策略.以CO2激光光束为热源,对探针针杆尖端进行加热,使针杆尖端受热融化产生微球.然后将带有微球的探针针杆绕其中轴线旋转180°,再使用CO2激光光束辐照带有微球的探针尖端,对尖端微球偏移量进行补偿.实验结果表明:采用“熔球-旋转再熔球”的两步法加工策略,能明显降低探针尖端微球相对于针杆的弯曲程度,缩小探针尖端球形球心和针杆中心线的偏移距离.     

新型光滑正则半监督SVM方法及其在信用评级中的应用

提出了一种基于光滑正则的半监督支持向量机方法,并将其用于建立中小信用评级模型.它从少量标签样本和大量无标签样本中构造反映数据流形结构的光滑正则项,并结合到支持向量机的最大间隔分类器的学习过程.然后,提出一种渐进式方法来迭代获得“半标签”样本,稳健地提升支持向量机的泛化性能.在真实数据集上的实验结果表明,新方法获得的测试精度显著优于多种现有方法,非常适用于中小企业的信用评级任务.     

弹性多核学习

多核学习 (MKL) 的提出是为了解决多个核矩阵的融合问题, 多核学习求解关于多个核矩阵的最优的线性组合并同时解出对应于这个组合矩阵的支持向量机(SVM)问题. 现有的多核学习的框架倾向于寻找稀疏的组合系数, 但是当有信息的核的比例较高的时候, 对稀疏性的倾向会使得只有少量的核被选中而损失相当的分类信息. 在本文中, 我们提出了弹性多核学习的框架来实现自适应的多核学习. 弹性多核学习的框架利用了一个混合正则化函数来均衡稀疏性和非稀疏性, 多核学习和支持向量机问题都可以视作弹性多核学习的特殊情形. 基于针对多核学习的梯度下降法, 我们导出了针对弹性多核学习的梯度下降法. 仿真数据的结果显示了弹性多核学习方法相对多核学习和支持向量机的优势; 我们还进一步将弹性多核学习应用于基因集合分析问题并取得了有意义的结果; 最后, 我们比较研究了弹性多核学习与另一种利用了非稀疏思想的多核学习.     

基于GL847的扫描图像校正

扫描仪在扫描成像过程中,诸多因素会给扫描图像带来误差和扭曲,因而必须对其加以校正。在分析扫描仪误差产生原理的基础上,详细讨论了基于GL847的扫描图像增益与偏移校正机制,提出了一种有效的扫描图像校正参数获取方法。     

Frequency domain regularization of d-dimensional structure tensor-based directional fields

The present work is intended to address two of the major difficulties that can be found when tackling the estimation of the local orientation of the data in a scene, a task which is usually accomplished by means of the computation of the structure tensor-based directional field. On one hand, the orientation information only exists in the non-homogeneous regions of the dataset, while it is zero in the areas where the gradient (i.e. the first-order intensity variation) remains constant. Due to this lack of information, there are many cases in which the overall shape of the represented objects cannot be precisely inferred from the directional field. On the other hand, the orientation estimation is highly dependent on the particular choice of the averaging window used for its computation (since a collection of neighboring gradient vectors is needed to obtain a dominant orientation), typically resulting in vector fields which vary from very irregular (thus yielding a noisy estimation) to very uniform (but at the expense of a loss of angular resolution). The proposed solution to both drawbacks is the regularization of the directional field; this process extends smoothly the previously computed vectors to the whole dataset while preserving the angular information of relevant structures. With this purpose, the paper introduces a suitable mathematical framework and deals with the d-dimensional variational formulation which is derived from it. The proposed formulation is finally translated into the frequency domain in order to obtain an increase of insight on the regularization problem, which can be understood as a low-pass filtering of the directional field. The frequency domain point of view also allows for an efficient implementation of the resulting iterative algorithm. Simulation experiments involving datasets of different dimensionality prove the validity of the theoretical approach.     

Relations Between Regularization and Diffusion Filtering

Regularization may be regarded as diffusion filtering with an implicit time discretization where one single step is used. Thus, iterated regularization with small regularization parameters approximates a diffusion process. The goal of this paper is to analyse relations between noniterated and iterated regularization and diffusion filtering in image processing. In the linear regularization framework, we show that with iterated Tikhonov regularization noise can be better handled than with noniterated. In the nonlinear framework, two filtering strategies are considered: the total variation regularization technique and the diffusion filter technique of Perona and Malik. It is shown that the Perona-Malik equation decreases the total variation during its evolution. While noniterated and iterated total variation regularization is well-posed, one cannot expect to find a minimizing sequence which converges to a minimizer of the corresponding energy functional for the Perona–Malik filter. To overcome this shortcoming, a novel regularization technique of the Perona–Malik process is presented that allows to construct a weakly lower semi-continuous energy functional. In analogy to recently derived results for a well-posed class of regularized Perona–Malik filters, we introduce Lyapunov functionals and convergence results for regularization methods. Experiments on real-world images illustrate that iterated linear regularization performs better than noniterated, while no significant differences between noniterated and iterated total variation regularization have been observed.     

工件坐标系编程的译码程序设计

数控系统对零件加工程序段中的坐标值译码最为复杂,采用C语言开发了数控系统中的译码程序,实现了工件坐标系下的编程译码,为今后实现更多编程方法提供了方便。