二维小波变换及在青藏高原地形重构中的应用

计算和检验了4种不同小波基底和不同阶小波基底对单脉冲和尖峰两个信号的分解及重构的性质,结果表明双正交小波的精度最高,Coifman小波的精度最低.通过设阈值对小波和快速Fourier变换进行截断后再重构,说明小波具有重构精度高、所用非零系数少以及误差被局域化等优点,这就削弱了"Gibbs现象",限制了它的影响范围.在此基础上,用二维快速Fourier和二维离散小波变换对实际青藏高原及其附近地形做了分解、重构及截断后重构等,说明二维小波变换能以较之FFT更少的非零系数和误差局域化等重构大地形,表明了二维小波变换在未来大气环流数值模式中的应用潜力.

Application of Two Dimensional Wavelet Transform in the Reconstruction of Tibetan Plateau Topography

A single pulse and peak signals are decomposed and reconstructed with four types of wavelet bases in different orders. Results demonstrate that the biorthogonal wavelet is of a best fitting to the signals, and the Coifman wavelet is at the last in the four bases. After truncating the expansion series of the wavelets and the Fourier transform, the reconstruction shows that the wavelet reconstruction got higher precision with less number of non-zero coefficients and the local error distribution compared with the Fast Fourier transform we calculated. Thus the wavelet reconstruction can greatly attenuate "Gibbs phenomenon" and limit the errors in a narrow domain around the singularities of the signals.Besides, we also make expansions for the topography of Tibetan plateau in wavelets and Fourier transform. Its reconstruction with or without truncation shows the similar features as the one-dimensional signal reconstruction above.