It is now widely recognized that the analysis of the intrinsic geometric characteristics of the underlying image is essential in many applications, including image processing. To achieve this, several directional schemes of image representation have been proposed. In this paper, we developed the discrete shearlet transform (DST) that provides an efficient multiscale directional representation and shows that the transform implementation is constructed in a discrete frame based multiresolution analysis (MRA). We evaluate the performance of DST in image removal and image approximation applications. In image approximations, our approach scheme using the DST exceeds the DWT, while the computational cost of our scheme is comparable to the DWT. In addition, in the elimination of images, the DST compares favorably with other transformations existing in the literature.