共查询到20条相似文献,搜索用时 15 毫秒
1.
利用多尺度随机模型能建立处理问题有效并行算法的这一优势,提出一类随机动态过程基于一般q阶树的多尺度建模方法。首先,利用Markov过程的条件独立性给出一类过程基于q阶树的多尺度表示方法;其次,基于q阶树多尺度表示和具体实例推导出多尺度模型中的状态转移矩阵、扰动阵、初始状态和相应的协方差矩阵等的具体形式,为具有Markov统计特性的过程或信号建立起多尺度随机模型,这将为有效地解决多源同类信息和多源异类信息的数据融合等实际问题提供了理论基础;最后,给出一类Gauss-Markov过程基于三阶树和五阶树多尺度表示的计算机仿真结果,进一步验证建立模型的实用性和有效性。 相似文献
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We consider the smoothing problem for multiscale stochastic systems based on the wavelet transform. These models involve processes indexed by the nodes of a dyadic tree. Each level of the dyadic tree represents one scale or resolution of the process; therefore, moving upward on the tree divides the resolution by 2, whereas moving downward multiplies it by 2. The processes are built according to a recursion in scale from coarse to fine to which random details are added. To operate the change in scale, one must perform an interpolation. This is achieved using the QMF pair of operators attached to a wavelet transform. These models have proved to be of great value to capture textures or fractal-like processes as well as to perform multiresolution sensor fusion (an example of which is given here). Up to now however, only subclasses of multiscale systems were amenable to fast algorithms and through different formalisms: those relying on Haar's wavelet and those involving only one of the two wavelet interpolators. We provide here a unifying framework that handles any system based on orthogonal wavelets. A smoothing theory is presented to define the field of fast algorithms for Markov random fields and give intuition on how to design them. This theory reveals the difficulties arising with general multiscale systems. We then prove that orthogonality properties of wavelets are the gate to fastness 相似文献
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Recently, a class of multiscale stochastic models has been introduced in which random processes and fields are described by scale-recursive dynamic trees. A major advantage of this framework is that it leads to an extremely efficient, statistically optimal algorithm for least-squares estimation. In certain applications, however, estimates based on the types of multiscale models previously proposed may not be adequate, as they have tended to exhibit a visually distracting blockiness. We eliminate this blockiness by discarding the standard assumption that distinct nodes on a given level of the multiscale process correspond to disjoint portions of the image domain; instead, we allow a correspondence to overlapping portions of the image domain. We use these so-called overlapping-tree models for both modeling and estimation. In particular, we develop an efficient multiscale algorithm for generating sample paths of a random field whose second-order statistics match a prespecified covariance structure, to any desired degree of fidelity. Furthermore, we demonstrate that under easily satisfied conditions, we can "lift" a random field estimation problem to one defined on an overlapped tree, resulting in an estimation algorithm that is computationally efficient, directly produces estimation error covariances, and eliminates blockiness in the reconstructed imagery without any sacrifice in the resolution of fine-scale detail. 相似文献
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Computationally Efficient Stochastic Realization for Internal Multiscale Autoregressive Models 总被引:4,自引:1,他引:4
In this paper we develop a stochastic realization theory for multiscale autoregressive (MAR) processes that leads to computationally efficient realization algorithms. The utility of MAR processes has been limited by the fact that the previously known general purpose realization algorithm, based on canonical correlations, leads to model inconsistencies and has complexity quartic in problem size. Our realization theory and algorithms addresses these issues by focusing on the estimation-theoretic concept of predictive efficiency and by exploiting the scale-recursive structure of so-called internal MAR processes. Our realization algorithm has complexity quadratic in problem size and with an approximation we also obtain an algorithm that has complexity linear in problem size. 相似文献
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Basseville M. Benveniste A. Willsky A.S. 《Signal Processing, IEEE Transactions on》1992,40(8):1915-1934
In many applications it is of interest to analyze and recognize phenomena occurring at different scales. The recently introduced wavelet transforms provide a time-and-scale decomposition of signals that offers the possibility of such analysis. A corresponding statistical framework to support the development of optimal, multiscale statistical signal processing algorithms is described. The theory of multiscale signal representation leads naturally to models of signals on trees, and this provides the framework for investigation. In particular, the class of isotropic processes on homogeneous trees is described, and a theory of autoregressive models is developed in this context. This leads to generalizations of Schur and Levinson recursions, associated properties of the resulting reflection coefficients, and the initial pieces in a system theory for multiscale modeling 相似文献
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Tretter D. Bouman C.A. Khawaja K.W. Maciejewski A.A. 《IEEE transactions on image processing》1995,4(12):1641-1654
We develop a novel multiscale stochastic image model to describe the appearance of a complex three-dimensional object in a two-dimensional monochrome image. This formal image model is used in conjunction with Bayesian estimation techniques to perform automated inspection. The model is based on a stochastic tree structure in which each node is an important subassembly of the three-dimensional object. The data associated with each node or subassembly is modeled in a wavelet domain. We use a fast multiscale search technique to compute the sequential MAP (SMAP) estimate of the unknown position, scale factor, and 2-D rotation for each subassembly. The search is carried out in a manner similar to a sequential likelihood ratio test, where the process advances in scale rather than time. The results of this search determine whether or not the object passes inspection. A similar search is used in conjunction with the EM algorithm to estimate the model parameters for a given object from a set of training images. The performance of the algorithm is demonstrated on two different real assemblies. 相似文献
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Wavelet-based identification of delamination defect in CMP (Cu-low k) using nonstationary acoustic emission signal 总被引:1,自引:0,他引:1
Ganesan R. Das T.K. Sikder A.K. Kumar A. 《Semiconductor Manufacturing, IEEE Transactions on》2003,16(4):677-685
Wavelet-based multiscale analysis approaches have revolutionized the tasks of signal processing, such as image and data compression. However, the scope of wavelet-based methods in the fields of statistical applications, such as process monitoring, density estimation, and defect identification, are still in their early stages of evolution. Recent literature contains some applications of wavelet-based methods in monitoring, such as tool-life monitoring, bearing defect monitoring, and monitoring of ultra-precision processes. This paper presents a novel application of a wavelet-based multiscale method in a nanomachining process [chemical mechanical planarization (CMP)] of wafer fabrication. The application involves identification of delamination defect of low-k dielectric layers by analyzing the nonstationary acoustic emission (AE) signal and coefficient of friction (CoF) signal collected during copper damascene (Cu-low k) CMP process. An offline strategy and a moving window-based strategy for online implementation of the wavelet monitoring approach are developed. Both offline and moving window-based strategies are implemented on the data collected from two different sources. The results show that the wavelet-based approach using the AE signal offers an efficient means for real-time detection of delamination defects in CMP processes. Such an online strategy, in contrast to the existing offline approaches, offers a viable tool for CMP process control. The results also indicate that the CoF signal is insensitive to delamination defect. 相似文献
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There has been a growing interest in synthetic aperture radar (SAR) imaging on account of its importance in a variety of applications. One attribute leading to its gain in popularity is its ability to image terrain at extraordinary rates. Acquiring data at such rates, however, has drawbacks in the form of exorbitant costs in data storage and transmission over relatively slow channels; thus, addressing these problems is clearly important. To abate these and related costs, we propose a segmentation-driven compression technique using hierarchical stochastic modeling within a multiscale framework. Our approach to SAR image compression is unique in that we exploit the multiscale stochastic structure inherent in SAR imagery. This structure is well captured by a set of scale auto-regressive (AR) models that accurately characterize the evolution in scale of homogeneous regions of different classes of terrain. We thus use them to generate a multiresolution segmentation of the image. The segmentation is subsequently used in tandem with the corresponding models in a pyramid encoder to provide a robust, hierarchical compression technique that, in addition to coding the segmentation, achieves high compression ratios with impressive image quality 相似文献
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《IEEE transactions on information theory / Professional Technical Group on Information Theory》1981,27(5):656-658
A mathematical treatment of the random field which we have used as a stochastic model for wind pressure exciting the ocean surface is presented. It is a composite stochastic process consisting of an infinite series of ordinary processes and point processes. It is shown that this is a well-defined homogeneous fourth-order random field. 相似文献
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Likelihood calculation for a class of multiscale stochastic models,with application to texture discrimination 总被引:4,自引:0,他引:4
A class of multiscale stochastic models based on scale-recursive dynamics on trees has previously been introduced. Theoretical and experimental results have shown that these models provide an extremely rich framework for representing both processes which are intrinsically multiscale, e.g., 1/f processes, as well as 1D Markov processes and 2D Markov random fields. Moreover, efficient optimal estimation algorithms have been developed for these models by exploiting their scale-recursive structure. The authors exploit this structure in order to develop a computationally efficient and parallelizable algorithm for likelihood calculation. They illustrate one possible application to texture discrimination and demonstrate that likelihood-based methods using the algorithm achieve performance comparable to that of Gaussian Markov random field based techniques, which in general are prohibitively complex computationally. 相似文献
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Multiscale autoregressive models and wavelets 总被引:4,自引:0,他引:4
Daoudi K. Frakt A.B. Willsky A.S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1999,45(3):828-845
The multiscale autoregressive (MAR) framework was introduced to support the development of optimal multiscale statistical signal processing. Its power resides in the fast and flexible algorithms to which it leads. While the MAR framework was originally motivated by wavelets, the link between these two worlds has been previously established only in the simple case of the Haar wavelet. The first contribution of this paper is to provide a unification of the MAR framework and all compactly supported wavelets as well as a new view of the multiscale stochastic realization problem. The second contribution of this paper is to develop wavelet-based approximate internal MAR models for stochastic processes. This will be done by incorporating a powerful synthesis algorithm for the detail coefficients which complements the usual wavelet reconstruction algorithm for the scaling coefficients. Taking advantage of the statistical machinery provided by the MAR framework, we will illustrate the application of our models to sample-path generation and estimation from noisy, irregular, and sparse measurements 相似文献
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Algorithms for multiscale basis selection and feature extraction for pattern classification problems are presented. The basis selection algorithm is based on class separability measures rather than energy or entropy. At each level the "accumulated" tree-structured class separabilities obtained from the tree which includes a parent node and the one which includes its children are compared. The decomposition of the node (or subband) is performed (creating the children), if it provides larger combined separability. The suggested feature extraction algorithm focuses on dimensionality reduction of a multiscale feature space subject to maximum preservation of information useful for classification. At each level of decomposition, an optimal linear transform that preserves class separabilities and results in a reduced dimensional feature space is obtained. Classification and feature extraction is then performed at each scale and resulting "soft decisions" obtained for each area are integrated across scales. The suggested algorithms have been tested for classification and segmentation of one-dimensional (1-D) radar signals and two-dimensional (2-D) texture and document images. The same idea can be used for other tree structured local basis, e.g., local trigonometric basis functions, and even for nonorthogonal, redundant and composite basis dictionaries. 相似文献
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Multiscale representations of Markov random fields 总被引:5,自引:0,他引:5
Luettgen M.R. Karl W.C. Willsky A.S. Tenney R.R. 《Signal Processing, IEEE Transactions on》1993,41(12):3377-3396
Recently, a framework for multiscale stochastic modeling was introduced based on coarse-to-fine scale-recursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. The authors show that this model class is also quite rich. In particular, they describe how 1-D Markov processes and 2-D Markov random fields (MRFs) can be represented within this framework. The recursive structure of 1-D Markov processes makes them simple to analyze, and generally leads to computationally efficient algorithms for statistical inference. On the other hand, 2-D MRFs are well known to be very difficult to analyze due to their noncausal structure, and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification. In contrast, their multiscale representations are based on scale-recursive models and thus lead naturally to scale-recursive algorithms, which can be substantially more efficient computationally than those associated with MRF models. In 1-D, the multiscale representation is a generalization of the midpoint deflection construction of Brownian motion. The representation of 2-D MRFs is based on a further generalization to a “midline” deflection construction. The exact representations of 2-D MRFs are used to motivate a class of multiscale approximate MRF models based on one-dimensional wavelet transforms. They demonstrate the use of these latter models in the context of texture representation and, in particular, they show how they can be used as approximations for or alternatives to well-known MRF texture models 相似文献
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基于随机共振电路模拟的微弱周期信号检测 总被引:2,自引:0,他引:2
采用电路模拟非线性Duffing振子,利用其随机共振机制来检测微弱周期信号。针对随机共振只适用于极低频输入信号的限制,引入一种适当的变量变换可以将高频信号转化成符合随机共振理论要求的低频信号进行处理,增强了该方法在工程应用中的可行性。采用电路模拟方法检测微弱周期信号,不需要象随机共振数值仿真所要求的那样对信号过采样,在满足采样定理的条件下,可以取较小的采样频率,降低了对硬件的要求。实验表明,该方法能有效地从强背景噪声中检测出微弱周期信号,在机械系统故障早期检测、化学谱信号提取、多传感器测量等领域有实际应用价值。 相似文献
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《IEEE transactions on image processing》2009,18(8):1724-1741
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Sun J. Gu D. Zhang S. Chen Y. 《Vision, Image and Signal Processing, IEE Proceedings -》2004,151(3):215-223
The authors propose a multiscale Bayesian texture segmentation algorithm that is based on a complex wavelet domain hidden Markov tree (HMT) model and a hybrid label tree (HLT) model. The HMT model is used to characterise the statistics of the magnitudes of complex wavelet coefficients. The HLT model is used to fuse the interscale and intrascale context information. In the HLT, the interscale information is fused according to the label transition probability directly resolved by an EM algorithm. The intrascale context information is also fused so as to smooth out the variations in the homogeneous regions. In addition, the statistical model at pixel-level resolution is formulated by a Gaussian mixture model (GMM) in the complex wavelet domain at scale 1, which can improve the accuracy of the pixel-level model. The experimental results on several texture images are used to evaluate the algorithm. 相似文献
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Navarro-Moreno J. Ruiz-Molina J.C. Fernandez-Alcala R.M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2003,49(6):1574-1578
Two distinct approximate series representations are obtained for the entire class of measurable, second-order stochastic processes defined on any interval of the real line. They include as particular cases all earlier approximate representations based on the Rayleigh-Ritz method. It is also shown that each of them converges with a different type of convergence. Finally, two applications in statistical communication theory are presented. 相似文献
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