Denoising of time series data based on Bayes models using wavelets

本研究的主要目的是减少时间序列数据中的噪声项。利用正交小波的正交矩阵对时间序列数据进行变换，得到小波系数。假设系数遵循贝叶斯模型，我们通过权衡参数保留/收缩/杀死系数。通过各种数值算例表明，该方法比文献中提出的方法有上级的优越性。我们在卫星数据分析方面的其他结果如下：-我们从Landsat的历史、数据采集系统、几何校正、去噪、数据融合和判别分析等方面讨论了Landsat数据分析。我们回顾并重新观察了这些观点，并以书籍的形式出版。关于土地覆盖分类，我们认为空间相关的正态分布和参数估计程序。多光谱数据的歧视由于马氏距离的惩罚似然。分类器可以利用混合训练数据以及纯细胞。通过数值研究，该分类器工作良好，特别是在未混合的情况下。关于数据融合技术，我们考虑了一种基于协克里格的方法。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方法具有更好的增强效果。我们还研究了基于AIC的变量选择标准，用于预测低分辨率图像。

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.