Data compression and harmonic analysis
IEEE Transactions on Information Theory
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
Directionlets: anisotropic multidirectional representation with separable filtering
IEEE Transactions on Image Processing
The Nonsubsampled Contourlet Transform: Theory, Design, and Applications
IEEE Transactions on Image Processing
Image separation using wavelets and shearlets
Proceedings of the 7th international conference on Curves and Surfaces
An edge detection algorithm based on the multi-direction shear transform
Journal of Visual Communication and Image Representation
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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 muItiscale 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.