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Some problems in statistics of random processes with applications to nonlinear filtering and image processing.

机译：随机过程统计中的一些问题在非线性滤波和图像处理中的应用。

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摘要

The thesis consists of three parts, all of which are concerned with approaches to the problem of filtering random processes or fields. However, methods employed differ substantially.; The first part builds on the well developed theory of linear Kalman filtering in order to adapt it to the setup and types of signals usually associated with non-parametric statistics. A class of signals possessing certain smoothness properties is considered, as well as cases with small noise and common noise. An adaptive filtering scheme is proposed which is then proved to be asymptotically equivalent to optimal kernel smoothing estimates usually used in non-parametric statistics.; The second part extends the traditional nonlinear filtering problem and the spectral separating scheme (S3) for an efficient numerical implementation in the case of distributed (field) observations. Connection of nonlinear filtering is exposed to matched filters commonly employed in engineering literature and practice.; Afterwards, the problem of increasing the precision of the spectral separating scheme is considered, and advantages of using wavelet bases in the scheme are discussed. Two examples arising from practical problems are presented.; The third part deals with modifications of the well-known Wald's (or Sequential Probability Ratio) Test and its applications to image processing. Reflected Wald's Test is introduced, consistency is proved for estimates based on it in the exponential and Gaussian noise cases. A new edge detection algorithm based on the Reflected Wald's Test is discussed.
机译：本文由三个部分组成，所有这些部分都与解决随机过程或字段的过滤问题有关。但是，所采用的方法大不相同。第一部分基于完善的线性卡尔曼滤波理论，以使其适应通常与非参数统计相关的信号的设置和类型。考虑了具有某些平滑性的一类信号，以及具有小噪声和普通噪声的情况。提出了一种自适应滤波方案，然后证明该方案渐近等效于通常用于非参数统计的最优核平滑估计。第二部分扩展了传统的非线性滤波问题和频谱分离方案（ S 3 ），以便在分布式（现场）观测情况下实现高效的数值实现。非线性滤波的连接暴露于工程文献和实践中常用的匹配滤波器。然后，考虑了提高频谱分离方案精度的问题，并讨论了在该方案中使用小波基的优点。给出了两个由于实际问题而产生的例子。第三部分介绍了对著名的Wald（或顺序概率比）测试及其在图像处理中的应用的修改。引入了反射Wald检验，证明了在指数和高斯噪声情况下基于估计的一致性。讨论了一种基于反射沃尔德检验的边缘检测算法。

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  • 作者

    Kligys, Skirmantas.;

  • 作者单位

    University of Southern California.;

  • 授予单位 University of Southern California.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 1998
  • 页码 128 p.
  • 总页数 128
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 统计学;
  • 关键词

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