二维图像小波分析的滤波器设计

滤波器的设计是实现二维图像小波分析的关键。在研究图像信号特征和一维小波变换理论的基础上，根据图像信号邻近像素的相关性提出了一种准对称边界延拓方法，用一维小波变换实现了二维离散小波变换，同时，在理论上证明了行的反向数据流的离散小波变换也是反向的，离散细节信号除反向外并改变符号的性质，并利用双正交滤波器的对称性建立了一种实现二维离散小波变换的滤波器结构，实现证明此方法有较好的图像重构性和信噪比。

Filter Design of Wavelet Transform for 2-D Image

The filter design is the key to 2-D image wavelet transform. Based on the studying of image properties and 1-D wavelet theory,the authors describe a parasymmetry boundary extension method and realize 2-D discrete wavelet transform by means of 1-D wavelet transform according to correlation of adjacent pixels. Also,it is proved that the discrete wavelet transform of inverse data stream in row and the sign of discrete detail signal will be inversed,and that a filter of wavelet transform based on symmetry of bi_orthogonal filter is constructed. The test has proved the fine reconstruction and perfect SNR.