切波构造的一个注记

Note on the Construction of Shearlets

切波构造通常依赖于2个函数ψ1(ω)和ψ2(ω),而它们均与满足一定条件的某个无穷次可微函数θ(x)的构造有关.2008年,Easley等给出了切波的一个例子.其中ψ1(ω)的构造比较简洁,而ψ2(ω)的构造过程比较繁琐.使用一种类似于ψ1(ω)的方法构造ψ2(ω)简化了Easley等的工作;同时定义了一类具有具体解析表达式的θ(x),最后用例子做了说明。

The construction of shearlets usually depends on two smooth functions Φ1 and Φ2.Φ1 and Φ2 are both associated with θ（x） that is certain infinitely differentiable function on real line R.In 2008,Easley gave an example of shearlets,where the strcture of Φ1 is simple and the construction process of Φ2 is relatively complicated.This paper provides another construction of Φ2,which simplifies Easley’s work.Then,a family of θ（x） is obtained in explicit expressions.Finally,some examples are presented.