基于格结构的三带小波构造及在图像融合中的应用

提出了一种构造具有正交性、对称性、紧支性以及较高消失矩的三带尺度滤波器与小波滤波器的方法.首先,通过设置尺度滤波器消失矩并转移尺度滤波器的对称性性质,有效地减少了构造尺度滤波器过程中未知量的个数以及计算推导过程的复杂度.在此基础上,利用格结构理论,给出了对具有仿酉特性的多相位矩阵的一种分解方法,并利用这种分解求出了冲击响应长度为9、消失矩为3以及响应长度为15、消失矩分别为3和4的小波滤波器.最后,把所求得的小波滤波器应用到多聚焦图像的融合中.实验结果表明,利用具有上述性质的三带小波进行图像融合可以得到比利用二带小波进行融合更好的效果.

Three-band wavelet construction based on lattice structure and its application in image fusion

An approach to construct a 3-band scaling filter and a wavelet filter was proposed,which not only is of orthogonality,symmetry and compact support but also has high vanishing moments.By setting the vanishing moment and switching the orthogonality of the scaling filter,this approach effectively reduces the number of unknown variables during the process of constructing the scaling filter and the complexity of the calculation process.Subsequently,a decomposition scheme of the polyphase matrix with paraunitary property was proposed on the basis of the lattice structure theory.Using this decomposition scheme,the corresponding wavelet filters are constructed whose impulse response length is 9 and vanishing moment is 3 and whose impulse response length is 15 and vanishing moment is 3 or 4,respectively.Finally,multi focus image fusion is implemented by using these wavelet filters.Experimental data show that the fusion result is better by using these 3-band wavelets than by using dyadic wavelets.