Flexible Wavelet Shrinkage for Nonparametric Mixed-Effects Models

• Main Authors: Fang-Jiun Lin, 林芳君
• Other Authors: Henry Horng-Shing Lu
• Format: Others
• Language: en_US
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/78539726393955224409

碩士 === 國立交通大學 === 統計所 === 88 === This article investigates the performance of a wavelet shrinkage method for signals and images based on the perspective of Bayes and empirical Bayes for nonparametric mixed-effects models (NPMEM). This is called BLUPWAVE because it is also the best linear unbiased prediction (BLUP) when the ratio of parameters for NPMEM is known. When the ratio is unknown, a nonlinear estimator guided by the oracle of BLUP has been derived. To make this nonlinear estimator adaptive and the data-driven selection of the level/subband dependent thresholds by generalized cross validation (GCV) is proposed. Furthermore, simultaneous selection of the primary resolution level and smoothness of wavelet basis is also discussed. The simulation studies of this adaptive BLUPWAVE and the soft thresholding by GCV for 1D signals and 2D images are compared by the standardized average squared error (SASE) in denoising and the compression ratio in compression. The theoretical comparison of compression ratios of BLUPWAVE vs. hard and soft thresholding are also discussed.