Shearlet is a new-style multi-scale geometry analysis tool. It creates Shearlet functions which have different characteristics through zooming

shearing

translating and other affine transforming methods

and enables its capable of optimally sparse representation. Firstly

a digital Shearlet transform implementation method is proposed in this paper. And then

a new de-noising method that combines Shearlet transform and variation is presented

which mainly been established using a total variation regularization model to constraint condition on Shearlet transform domain. The proposed model aims at reducing Pseudo-Gibbs artifacts after simple threshold methods. Numerical examples demonstrate that the method can remove noises and keep edges effectively

leading to improved visual effect and PSNR.