Image denoising with complex ridgelets

In this paper, we propose a novel image denoising method by incorporating the dual-tree complex wavelets into the ordinary ridgelet transform. The approximate shift invariant property of the dual-tree complex wavelet and the high directional sensitivity of the ridgelet transform make the new method a very good choice for image denoising. We apply the digital complex ridgelet transform to denoise some standard images corrupted with additive white noise. Experimental results show that the new method outperforms VisuShrink, the ordinary ridgelet image denoising, and wiener2 filter both in terms of peak signal-to-noise ratio and in visual quality. In particular, our method preserves sharp edges better while removing white noise. Complex ridgelets could be applied to curvelet image denoising as well.     

区间二型模糊集和模糊系统: 综述与展望

一型模糊集可以建模单个用户的语义概念中的不确定性, 即个体内不确定性. 一型模糊系统在控制和机器学习中得到了大量成功应用. 区间二型模糊集能同时建模个体内不确定性和个体间不确定性, 因而在很多应用中显示了比一型模糊系统更好的性能, 是近年来的研究热点. 本文首先介绍了区间二型模糊集的重要概念和理论研究进展, 总结了其在决策和机器学习中的成功应用, 然后介绍了区间二型模糊系统的基本操作和理论研究进展, 并回顾了其在控制和机器学习中的典型应用. 最后, 对区间二型模糊集和模糊系统未来的研究方向进行了展望.     

二元树复小波变换及其在图象方向滤波中的应用

复小波变换虽然具有良好的方向选择性和平移不变性 ,但不具备完全重构性条件 ,而二元树复小波变换(DTCWT)正好解决了这一难题 .在分析二元树复小波分解后的 12个高频子带方向性的基础上 ,利用其良好的方向选择性提出了一种对线形纹理图象进行增强滤波的方法 .该方法借助于小波变换域的方向解析性 ,在各子带中保留图象中各局部主方向的信息而滤除其他方向的噪声 .利用该方法进行滤波还可以避免对信号和噪声频率特性和统计特性进行估计 ,从而大大减小了滤波的复杂程度 .以指纹图象为例的实验结果表明 ,该方法效果较好 ,便于实现 ,尤其适用于噪声特性复杂的纹理图象的滤波 .     

基于特性分析的小波图像压缩性能研究

图象压缩时如何选择小波基是一个难题,这是由于不同的小波数学特性会对图象的压缩编码产生不同的影响.文中对小波基的正交性、光滑性、消失矩、滤波器长度等一些重要的小波特性对图象压缩性能的影响进行了对比研究.通过仿真分析,得出双正交小波比正交小波具有更优异的性能,一般条件下应尽量选择消失矩大、正则性好的双正交小波,而且应尽量优先保证重构小波的正则性效应,这样才可能得到效果较好的重构图像质量.但是在相同或相似的正则性、消失矩、滤波器长度等条件下,双正交小波较正交小波的性能改进则不是很明显.     

基于自适应检测长度的双门限能量感知算法

针对认知环境中能量感知的噪声不确定性问题,提出了一种基于自适应检测长度的双门限能量感知算法。算法首先根据噪声不确定性大小设置上下判决门限。当检测统计量位于双门限之外时直接判决,否则增加采样数并再次比较,直到得出判决结果或采样数达到上限;为了尽量减小由于采样数增加带来的系统能量开销的增加,给出了系统能量开销与吞吐量折中的最佳采样数上限。从理论上分析了算法的优越性,并进行了仿真验证,结果表明,该算法尽管增加了一定的能量开销,但是可以显著地提高系统检测性能。     

Interval set clustering

Rough k-means clustering describes uncertainty by assigning some objects to more than one cluster. Rough cluster quality index based on decision theory is applicable to the evaluation of rough clustering. In this paper we analyze rough k-means clustering with respect to the selection of the threshold, the value of risk for assigning an object and uncertainty of objects. According to the analysis, clusters presented as interval sets with lower and upper approximations in rough k-means clustering are not adequate to describe clusters. This paper proposes an interval set clustering based on decision theory. Lower and upper approximations in the proposed algorithm are hierarchical and constructed as outer-level approximations and inner-level ones. Uncertainty of objects in out-level upper approximation is described by the assignment of objects among different clusters. Accordingly, ambiguity of objects in inner-level upper approximation is represented by local uniform factors of objects. In addition, interval set clustering can be improved to obtain a satisfactory clustering result with the optimal number of clusters, as well as optimal values of parameters, by taking advantage of the usefulness of rough cluster quality index in the evaluation of clustering. The experimental results on synthetic and standard data demonstrate how to construct clusters with satisfactory lower and upper approximations in the proposed algorithm. The experiments with a promotional campaign for the retail data illustrates the usefulness of interval set clustering for improving rough k-means clustering results.     

多小波变换的提升格式及其在图象编码中的应用

在简要介绍提升格式和多小波之后，提出了一种新的实现多小波变换的提升格式模型，由于这个模型主要由若干个单小波变换的提升格式搭建而成，因而不必自己推演提升格式的内部结构和参数，另外，这个模型还可以根据实际应用的需要选用不同的单小波，该文还给出用D9／7双正交（单）小波变换的提升格式构造的多小波变换的实例，并把这样构造的多小波变换应用于图象编码，结果表明，该方法可取得比常用的GHM多小波图象编码更好的效果。     

Possibility and Necessity Pattern Classification using an Interval Arithmetic Perceptron

In the work presented in this paper, an Interval Arithmetic Perceptron (IAP) is used to detect the region in the input space to which an uncertainty decision should be appropriately associated. This region may be originated both by sub-regions which are not represented in the training set, and by subregions where the probabilities of the two classes are very similar. To train the IAP, an algorithm will be presented which in particular is able detect the two certainty regions and the uncertainty one From the interval weights thus obtained, a confidence interval of the probability will also be evaluated. The algorithm has been used for studying a simple artificial problem and two real-world appli-cations, the Iris and Breast Cancer databases. Regarding the latter application in particular, a statistical analysis of the results is presented, together with a discussion of the possible alternative classifications of the patterns attributed to the uncertainty region.     

基于复数小波的图像恢复算法研究

研究了基于复数小波的各种图像恢复算法，提出把HMT模型应用到ForWaRD的图像恢复中．利用ForWaRD算法，首先把模糊加噪的降质图像在傅立叶域中进行维纳滤波器正则反卷，然后在小波域中进行去噪处理，可以得到较好的恢复效果．对典型卷积加噪线性降质图像进行了仿真实验，并把基于复数小波的各种图像恢复算法的仿真结果同基于正交小波的图像恢复算法仿真结果作了比较，发现前者无论从客观指标还是视觉效果上都有明显的优势，尤其是基于HMT模型的复数ForWaRD图像恢复方法．     

Passive Control for Stochastic Interval Systems with Interval Time‐Varying Delay

This paper is concerned with the problem of delay‐dependent passive analysis and control for stochastic interval systems with interval time‐varying delay. The system matrices are assumed to be uncertain within given intervals, and the time delay is a time‐varying continuous function belonging to a given range. By the transformation of the interval uncertainty into the norm‐bounded uncertainty, partitioning the delay into two segments of equal length, and constructing an appropriate Lyapunov–Krasovskii functional in each segment of the delay interval, delay‐dependent stochastic passive control criteria are proposed without ignoring any useful terms by considering the information of the lower bound and upper bound for the time delay. The main contribution of this paper is that a tighter upper bound of the stochastic differential of Lyapunov–Krasovskii functional is obtained via a newly‐proposed bounding condition. Based on the criteria obtained, a delay‐dependent passive controller is presented. The results are formulated in terms of linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness of the method.     

Lifting Scheme及其在小波图象编码中的应用

Lifting Scheme是构造第二代小波的关键技术。相对于第一代小波而言,Lifting Scheme是一种比Mallat算法更快、更简单和更容易操作的算法,也是JPEG2000推荐的算法,为了将其应用到小波图象编码中,提出了一种对Lifting Scheme作适当改进以用于小波图象编码的方法。该方法就是先用Lifting Scheme来实现D9/7双正交小波变换,然后再用这种技术实现的D9/7双正交小波变换来进行图象压缩编码。在将Lifting Scheme算法用于小波图象编码的过程中,对该算法做了必要的简化,以便保证每个提升(lifting）环节都是FIR滤波。同时,根据能量守恒的原则,重新调整了尺度因子。实验结果表明,这种经过改进的Lifting Scheme取得了比Mallat算法更好的图象编码效果。     

Interval prediction of responses for uncertain multidisciplinary system

Considering that numerous sample data points are required in the probabilistic method, a non-probabilistic interval analysis method can be an alternative when the information is insufficient. In the paper, new strategies, which are iterative algorithm based interval uncertainty analysis methods (IA-IUAMs), are developed to acquire the bounds of the responses in multidisciplinary system. Two iterative processes, Jacobi iteration and Seidel iteration, are applied in the new methods respectively. The Jacobi iteration based interval uncertainty analysis method (JI-IUAM) utilizes the strategy of concurrent subsystem analysis to improve computational efficiency while the Seidel iteration based interval uncertainty analysis method (SI-IUAM) can accelerate convergence by utilizing the newest information. Both IA-IUAMs are able to evaluate the bounds of responses accurately and quickly. The presented methods are compared with general sensitivity analysis based interval uncertainty analysis method (SIUAM) and conventional Monte Carlo simulation approach (MCS). The validity and efficiency of the new methods are demonstrated by two numerical examples and two engineering examples. Results show that, on the one hand, IA-IUAMs are more efficient than MCS by avoiding hundreds of system analyses, on the other hand, IA-IUAMs are more accurate and have a wider range of application than SIUAM by avoiding linear approximation and global sensitivity calculation.     

噪声环境中时延区间CNN网络鲁棒稳定性

由于采用大规模集成电路方法实现细胞神经网络(cellular neural networks,CNN),其 电路所产生的噪声不可避免,实际的网络都是在噪声环境中进行工作的,弄清楚这些随机干扰 是如何影响网络的稳定性,在网络设计时非常关键.利用鞅收敛定理、李雅普诺夫直接法和矩阵 分析的方法,研究了白噪声干扰下时延区间细胞神经网络承受扰动的能力,得到了仅依赖系统 参数的充分性代数判据.所得结果在系统设计时检验较为方便.     

二维二通道小波的构造与图像融合应用

提出了一类新的二维二通道小波的一种构造方法，并把此类小波应用于图像融合中，提出了利用小波分解后的低频子图像的梯度图对高频子图像进行融合的图像融合算法，并采用熵、均方根误差等指标对融合结果图像进行了评价。实验结果表明，该方法有较好的视觉效果。其融合性能好于采用相同融合算法的基于张量积四通道小波的融合方法，并能节约50%的运算量。     

基于区间数聚类的无线传感器网络定位方法

在基于接收信号强度指示(Received signal strength indicator, RSSI) 测距的无线传感器网络(Wireless sensor network, WSN)定位方法应用过程中, 信号强度与对应通信距离的对数成线性关系的假设在实际无线通信环境下几乎不能满足, 从而导致定位误差较大. 针对此问题, 本文首先利用区间数表示方法结合实际定位环境中RSSI数据的统计信息表示RSSI的分布区域, 并采用区间数聚类方法实现距离估计, 以减小由于RSSI值不确定性引起的距离估计误差, 然后利用这些距离估计值实现基于测距的WSN定位方法. 采用三种实际通信环境下RSSI测量数据完成的定位实验结果表明, 本文提出的基于区间数聚类RSSI-通信距离(RSSI-D)估计的定位方法可有效地提高定位精度.     

Interval consensus problem of multi-agent systems in accordance with switching protocol

In this paper, we discuss the interval consensus problem of multi-agent systems by providing a special Laplacian of directed graphs. As one of the most important issues in the coordination control of multi-agent systems, the consensus problem requires that the output of several spatially distributed agents reach a common value that depends on the states of all agents. For the given consensus protocol and initial states, a fixed consensus value is obtained. The resulting consensus value, however, may not be ideal or meet the quality that we require from the multi-agent system. In this paper, by introducing two state-dependent switching parameters into the consensus protocol, the system given by the proposed protocol can globally asymptotically converge to a designated point on a special closed and bounded interval. In other words, the system given by the proposed protocol can globally asymptotically reach interval consensus and then the system can also achieve a generalised interval average consensus if the directed graph is balanced. Simulations are presented to demonstrate the effectiveness of our theoretical results.     

Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 2, Inverse Problems

In Part 1 of this two-part paper, we bounded the centroid of a symmetric interval type-2 fuzzy set (T2 FS), and consequently its uncertainty, using geometric properties of its footprint of uncertainty (FOU). We then used these bounds to solve forward problems, i.e., to go from parametric interval T2 FS models to data. The main purpose of the present paper is to formulate and solve inverse problems, i.e., to go from uncertain data to parametric interval T2 FS models, which we call type-2 fuzzistics. Given interval data collected from people about a phrase, and the inherent uncertainties associated with that data, which can be described statistically using the first- and second-order statistics about the end-point data, we establish parametric FOUs such that their uncertainty bounds are directly connected to statistical uncertainty bounds. These results should find applicability in computing with words     

基于VPRS粗糙熵的图像分割

变精度粗糙集是解决模糊决策问题的重要工具，图像边缘信息本身就具有一定的不确定性和模糊性，而图像分割的效果直接依赖于对图像边缘像素的判断精度，因此变精度粗糙集可以更精确地表达图像边缘。将经典图像粗糙集模型扩展到图像变精度粗糙集模型，并将其应用于灰度图像边缘判定问题，利用变精度粗糙集的上下近似定义，构造了变精度灰色形态学算子，依据灰度图像粗糙熵的定义，提出一种基于VPRS粗糙熵的图像分割算法。针对噪声图像，该方法用变精度粗糙集模型判断目标、背景和边界像素集，在不同参数下判断近似集时容忍部分噪声点的存在，从而可获得较好的灰色边缘图像。实验结果说明，由于变精度灰度形态学算子避免了复杂参数优化过程，算法时间执行效率高；同时由于粗糙形态学算子对噪声的优良处理能力，新算法具有较好的噪声鲁棒性。     

基于区间数的多维不确定性数据UID-DBSCAN聚类算法

不确定性数据聚类方法的研究日益受到广泛关注,其中UIDK-means算法与U-PAM算法继承了基于划分算法无法识别任意形状簇和对噪声点敏感的缺陷。FDBSCAN算法事先假定不确定性数据的概率分布函数或概率密度函数是已知的,然而这些信息在实际应用中往往难以获取。针对上述算法的不足,提出一种基于区间数的多维不确定性数据聚类UID-DBSCAN算法。该算法利用区间数结合数据的统计信息合理地表示不确定性数据,采用低计算复杂度的区间数距离函数衡量不确定性数据对象间的相似度,首次提出区间数的密度、密度可达与密度相连等概念,并将其用于扩展簇中,同时结合数据集的统计特征自适应地选取算法的密度参数来实现自动聚类。实验结果表明,UID-DBSCAN算法能够有效识别噪声,处理任意形状簇,具有较高的聚类精度和较低的计算复杂度。