An edge-sensing predictor in wavelet lifting structures for lossless image coding
Journal on Image and Video Processing
R-D optimized tree-structured compression algorithms with discrete directional wavelet transform
Journal of Computational and Applied Mathematics
Image and video denoising using adaptive dual-tree discrete wavelet packets
IEEE Transactions on Circuits and Systems for Video Technology
Low-complexity iris coding and recognition based on directionlets
IEEE Transactions on Information Forensics and Security
Multiresolution image representation using combined 2-D and 1-D directional filter banks
IEEE Transactions on Image Processing
Geometric video approximation using weighted matching pursuit
IEEE Transactions on Image Processing
Tree-based wavelets for image coding: orthogonalization and tree selection
PCS'09 Proceedings of the 27th conference on Picture Coding Symposium
Design of directional filter banks with arbitrary number of subbands
IEEE Transactions on Signal Processing
Wavelet steerability and the higher-order Riesz transform
IEEE Transactions on Image Processing
Discrete directional wavelet image coder based on fast R-D optimized quadtree decomposition
ICIC'07 Proceedings of the intelligent computing 3rd international conference on Advanced intelligent computing theories and applications
Adaptive directional wavelet transform using pre-directional filtering
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Directional wavelet transforms for prediction residuals in video coding
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Low-complexity iris recognition with oriented wavelets
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Direction-adaptive context modeling for sign coding in embedded wavelet image coder
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Adaptive directional wavelet transform based on directional prefiltering
IEEE Transactions on Image Processing
Combining local filtering and multiscale analysis for edge, ridge, and curvilinear objects detection
IEEE Transactions on Image Processing
Directional lapped transforms for image coding
IEEE Transactions on Image Processing
Edge-preserving depth-map coding using graph-based wavelets
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
The discrete shearlet transform: a new directional transform and compactly supported shearlet frames
IEEE Transactions on Image Processing
Adaptive 2-D wavelet transform based on the lifting scheme with preserved vanishing moments
IEEE Transactions on Image Processing
Journal of Approximation Theory
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In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based perfect reconstruction and critically sampled anisotropic M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional WT, unlike in the case of some other directional transform constructions (e.g., curvelets, contourlets, or edgelets). The corresponding anisotropic basis functions (directionlets) have directional vanishing moments along any two directions with rational slopes. Furthermore, we show that this novel transform provides an efficient tool for nonlinear approximation of images, achieving the approximation power O(N-1.55), which, while slower than the optimal rate O(N-2), is much better than O(N-1) achieved with wavelets, but at similar complexity.