This paper describes a new pruned dual-tree discrete wavelet transform (DWT), which is designed to reduce the redundancy while maintaining the orientations. The new transform is based on the dual-tree wavelet transform introduced by Kingsbury. The number of wavelets associated with the transform is reduced substantially for both 2D and 3D cases. Wavelets generated from the pruned dual-tree DWT have direction/motion selectivity and are free of the checkerboard
artifact, which are efficient for signal applications, such as image and video processing. This paper also describes an algorithm to compute the Matching Pursuit decomposition with this transform. Examples are shown to illustrate the performance of the matching pursuit algorithm and the 2D and 3D pruned dual-tree wavelet transforms.