Optimally Sparse Image Representations using Shearlets

It is now widely acknowledged that traditional wavelets are not very effective in dealing with multidimensional signals containing distributed discontinuities. This paper presents a new discrete multiscale directional representation called the discrete shearlet transform. This approach, which is based on the shearlet transform previously developed by the authors and their colaborators, combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing images containing edges. Numerical experiments demonstrate that the discrete shearlet transform is very competitive in denoising applications both in terms of performance and computational efficiency.