A Class of Multiresolution Directional Filter Banks

• Published in: IEEE transactions on signal processing Vol. 55; no. 3; pp. 949 - 961
• Main Authors: Nguyen, T.T., Oraintara, S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-03-2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Banks; Construction; Continuous wavelet transforms; Contourlet; curvelet; Decomposition; Detection, estimation, filtering, equalization, prediction; diamond filter; directional decomposition; directional filter bank (DFB); Exact sciences and technology; Feature extraction; Filter bank; Filter banks; Frequency; Image processing; Image reconstruction; Information, signal and communications theory; Merging; Miscellaneous; multidimensional filter bank; Multidimensional systems; multiresolution directional filter bank (DFB); multiresolution representation; nonlinear approximation; Nonuniform; Partitioning; permissibility; quincunx; Signal and communications theory; Signal processing; Signal resolution; Signal, noise; Studies; Telecommunications and information theory; Tree data structures; Trees; Visual perception; Wavelet; quincunx; Partition method; Image processing; curvelet; Information extraction; directional filter bank (DFB); Multiresolution analysis; Implementation; diamond filter; multiresolution directional filter bank (DFB); Discrete filter; directional decomposition; Filter bank; multidimensional filter bank; Subband decomposition; nonlinear approximation; permissibility; Contourlet; Tree structure; multiresolution representation; Wavelet transformation; Quincunx mode; Signal processing; wavelet; Feature extraction; Decimation; Image denoising
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2006.887140

In this paper, we introduced a class of directional filter banks (DFBs) having the previously proposed uniform DFB (uDFB) as a special case. Except for the uDFB, each DFB in this class can be used to decompose an image yielding up to 12 directions while maintaining perfect reconstruction and maximal decimation. A multiresolution representation can be obtained by repeating the same decomposition at the lowpass band. The permissible property of the filter banks in cases of being implemented by a tree structure and by direct implementation is discussed. The result shows that only one DFB in the class, called the uniform quincunx DFB (uqDFB), satisfies the permissible property when being implemented directly without using the tree structure. The nonuniform quincunx DFB (nuqDFB) is then constructed from the uqDFB by merging its two lowpass subbands. An alternative structure for constructing the nuqDFB is presented. The new structure, while yielding the same frequency partitioning, allows the DFB to be realized with complexity comparable to that of the separable wavelet filter bank. The connection between the discrete filter bank and the continuous directional wavelet is also established. Numerical experiments on directional feature extractions, image denoising and nonlinear approximation are presented at the end of the paper to demonstrate the potential of the nuqDFB