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It is now widely acknowledged that analyzing the intrinsic geometrical features of the underlying image is essential in many applications including image processing. In order to achieve this, several directional image representation schemes have been proposed. In this paper, we develop the discrete shearlet transform (DST) which provides efficient multiscale directional representation and show that the implementation of the transform is built in the discrete framework based on a multiresolution analysis (MRA). We assess the performance of the DST in image denoising and approximation applications. In image approximations, our approximation scheme using the DST outperforms the discrete wavelet transform (DWT) while the computational cost of our scheme is comparable to the DWT. Also, in image denoising, the DST compares favorably with other existing transforms in the literature.