Denoising of time series data based on Bayes models using wavelets

本研究的主要目的是降低时间序列数据中的噪声项。利用小波的正交性对时间序列数据进行正交矩阵变换，得到小波系数。假设系数服从贝叶斯模型，我们通过权衡参数来保持/收缩/删除系数。通过各种数值算例表明，该方法优于文献中提出的方法。与卫星数据分析相关的其他结果如下：-我们从多个方面讨论了陆地卫星数据分析，陆地卫星的历史、数据采集系统、几何校正、去噪、数据融合和判别分析。我们对这些点进行了回顾和新的观察，并以书籍的形式发表。-关于土地覆盖分类，我们考虑了空间相关的正态分布，并开发了参数估计程序。多光谱数据通过由于马氏距离而受到惩罚的似然来区分。该分类器既可以利用混合训练数据，也可以利用纯细胞。通过数值实验表明，该分类器效果良好，尤其是在非混合情况下。-在数据融合技术方面，我们考虑了一种基于协同克立格的方法。实验结果表明，该方法比目前广泛应用于低分辨率彩色图像增强的HSV方法具有更好的性能。我们还研究了基于AIC的低分辨率图像预测的变量选择准则。

The main aim of this study is to reduce noise terms in time series data. We transform the time-series data by the orthogonal matrix due to orthogonal wavelets and obtain wavelet coefficients. Assuming the coefficients follow Bayes models, we keep/shrink/kill the coefficients through the trade-off parameter. It is shown through various numerical examples that the procedure is superior to those proposed in the literature.Our other results related to the satellite data analysis are as follows :- We discuss Landsat data analysis from various aspects ; history of Landsat, data acqusition system, geometric correction, denoising, data fusion and discriminant analysis. We reviewed and newly observed these points, and publish them in book form.- Concerning land-cover classifications, we consider spatially-correlated normal distributions and develop parameter estimation procedure. The multispectrum data are discriminated by a penalized likelihood due to Mahalanobis distance. The classifier can utilize mixel traing data as well as pure cells. By numerical study, the classifier works well, especially in unmixing case.- Concerning data fusion techniques, we consider a method based on cokriging. It is shown that the method shows better performance than HSV method which is widely used for enhancement of low-resolution colored images. We also examined variable selection criterion based on AIC for prediction of low-resolution images.