Discrete Shearlet Transform : New Multiscale Directional Image Representation

It is now widely acknowledged that analyzing the intrinsic geometrical features of an underlying image is essentially needed in image processing. In order to achieve this, several directional image representation schemes have been proposed. In this report, we develop the discrete shearlet transform (DST) which provides efficient multiscale directional representation. We also show that the implementation of the transform is built in the discrete framework based on a multiresolution analysis. We further assess the performance of the DST in image denoising and approximation applications. In image approximation, our adaptive approximation scheme using the DST significantly outperforms the wavelet transform (up to 3.0dB) and other competing transforms. Also, in image denoising, the DST compares favorably with other existing methods in the literature.