In order to obtain better smooth effect in signal or imagereconstruction

the regularity or continuous differentiability of wavelet mustbe increased as much as possible. The selection of sigmoid function in Meyer wavelet constructionaffects the differentiability

smoothness and attenuation speed of Meyerwavelet

so it is exceedingly essential to select sigmoid function. Firstly

a method of constructing fully smooth sigmoid function is given

and asufficiently smooth non-polynomial sigmoid function is taken as an example

which is usedas the excitation function in BP neural network for function approximation toobtain good approximation results. Then

the scale functions of Meyer wavelets are obtained by fullysmooth sigmoid functions. Meyer wavelets with limited spectrum are given with sufficientsmooth

high-ordervanishing moments and infinitesimal differentiability. Finally

the full smooth Meyerwavelet and the shearlet transform are combined to denoise the image. Comparedwith the traditional Meyer wavelet shearlet transform

the peak signal-to-noiseratio is higher and the denoised image texture and edge information are morecomplete.