Note on the Construction of Shearlets

The construction of shearlets usually depends on two smooth functions ψ₁ and ψ₂.ψ₁ and ψ₂ 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 ψ₁ is simple and the construction process of ψ₂ is relatively complicated.This paper provides another construction of ψ₂,which simplifies Easley's work.Then,a family of θ(x) is obtained in explicit expressions.Finally,some examples are presented.