中文摘要：

针对二元小波框架在图像处理中应用的有效性,本文研究二元最小能量小波框架的特征.给出二元最小能量小波框架存在的充分必要条件,刻画了二元最小能量小波框架的特征.通过对加细函数和小波函数对应的面具函数进行多相分解,提出二元最小能量小波框架的分解与重构算法,并给出数值算例.

英文摘要：

Aiming at the effective application for the bivariate wavelet frames in image procession,we investigate the properties of minimum-energy bivariate wavelet frames. The sufficient and necessary conditions on the existence for the minimum-energy bivariate wavelet frames are established. The characterization for minimum energy bivariate wavelet frames is performed. Decomposition and reconstruction algorithms for minimum-energy bivariate wavelet frames are formulated by implementing the polyphase decomposition on the mask functions that correspond to the refinable functions and the wavelet functions.Two numerical examples are provided.