Dense grid framelets with symmetric lowpass and bandpass filters

The paper presents new tight frame dyadic limit functions with dense time-frequency grid. The underlying lowpass and band-pass filters possess linear phase. The filterbank has additionally two highpass filters which are identical within one sample shift. This leads to wavelets which approximate shift-invariance. The filters in this paper are FIR and have vanishing moments.

[1]  Ivan W. Selesnick,et al.  A Higher Density Discrete Wavelet Transform , 2006, IEEE Transactions on Signal Processing.

[2]  A. Farras Abdelnour,et al.  Symmetric tight frame with shifted wavelets , 2005, SPIE Optics + Photonics.

[3]  I. Selesnick,et al.  Symmetric wavelet tight frames with two generators , 2004 .

[4]  Qingtang Jiang,et al.  Parameterizations of Masks for Tight Affine Frames with Two Symmetric/Antisymmetric Generators , 2003, Adv. Comput. Math..

[5]  Petukhov,et al.  Constructive Approximation Symmetric Framelets , 2003 .

[6]  C. Burrus,et al.  Introduction to Wavelets and Wavelet Transforms: A Primer , 1997 .

[7]  C. Chui,et al.  Compactly supported tight frames associated with refinable functions , 2000 .

[8]  Ivan W. Selesnick,et al.  Symmetric nearly shift-invariant tight frame wavelets , 2005, IEEE Transactions on Signal Processing.

[9]  Ioannis A. Kakadiaris,et al.  Image denoising using a tight frame , 2005, IEEE Transactions on Image Processing.

[10]  Helmut Bölcskei,et al.  Frame-theoretic analysis of oversampled filter banks , 1998, IEEE Trans. Signal Process..

[11]  Zheng-Xing Cheng,et al.  The construction of M-band tight wavelet frames , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

[12]  Fabrizio Argenti,et al.  Signal-dependent noise removal in the undecimated wavelet domain , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[13]  O. Herrmann On the approximation problem in nonrecursive digital filter design , 1971 .

[14]  Christine Fernandez-Maloigne,et al.  Undecimated wavelet shrinkage estimate of the 1D and 2D spectra , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).