Fan Hong-Yi, Lu Hai-Liang
Department of Physics, Shanghai Jiao Tong University, Shanghai, China.
Opt Lett. 2006 Dec 1;31(23):3432-4. doi: 10.1364/ol.31.003432.
Usually a wavelet transform is based on dilated-translated wavelets. We propose a symplectic-transformed-translated wavelet family psi()(r,s)(z-kappa) (r,s are the symplectic transform parameters, |s|(2)-|r|(2)=1, kappa is a translation parameter) generated from the mother wavelet psi and the corresponding wavelet transformation W(psi)f(r,s;kappa)=integral(infinity)(-infinity)(d(2)z/pi)f(z)psi()(r,s)(z-kappa). This new transform possesses well-behaved properties and is related to the optical Fresnel transform in quantum mechanical version.
通常，小波变换基于伸缩平移小波。我们提出了一个由母小波ψ生成的辛变换平移小波族ψ*(r,s)(z - κ)（r、s是辛变换参数，|s|² - |r|² = 1，κ是平移参数）以及相应的小波变换W(ψ)f(r,s;κ)=∫(-∞)(∞)(d²z/π)f(z)ψ*(r,s)(z - κ)。这种新变换具有良好的性质，并且在量子力学版本中与光学菲涅耳变换相关。
