TY - JOUR
T1 - Tight wavelet filter banks with prescribed directions
AU - Hur, Youngmi
N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.
PY - 2022/7/1
Y1 - 2022/7/1
N2 - Constructing tight wavelet filter banks with prescribed directions is challenging. This paper presents a systematic method for designing a tight wavelet filter bank, given any prescribed directions. There are two types of wavelet filters in our tight wavelet filter bank. One type is entirely determined by the prescribed information about the directionality and makes the wavelet filter bank directional. The other type helps the wavelet filter bank to be tight. In addition to the flexibility in choosing the directions, our construction method has other useful properties. It works for any multidimension, and it allows the user to have any prescribed number of vanishing moments along the chosen directions. Furthermore, our tight wavelet filter banks have fast algorithms for analysis and synthesis. Concrete examples are given to illustrate our construction method and properties of resulting tight wavelet filter banks.
AB - Constructing tight wavelet filter banks with prescribed directions is challenging. This paper presents a systematic method for designing a tight wavelet filter bank, given any prescribed directions. There are two types of wavelet filters in our tight wavelet filter bank. One type is entirely determined by the prescribed information about the directionality and makes the wavelet filter bank directional. The other type helps the wavelet filter bank to be tight. In addition to the flexibility in choosing the directions, our construction method has other useful properties. It works for any multidimension, and it allows the user to have any prescribed number of vanishing moments along the chosen directions. Furthermore, our tight wavelet filter banks have fast algorithms for analysis and synthesis. Concrete examples are given to illustrate our construction method and properties of resulting tight wavelet filter banks.
KW - Directional wavelet filters
KW - filter banks
KW - tight wavelet filter banks
KW - tight wavelet frames
KW - trigonometric polynomial sum of hermitian squares
KW - wavelet filters
KW - wavelets
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U2 - 10.1142/S0219691322500084
DO - 10.1142/S0219691322500084
M3 - Article
AN - SCOPUS:85129089709
SN - 0219-6913
VL - 20
JO - International Journal of Wavelets, Multiresolution and Information Processing
JF - International Journal of Wavelets, Multiresolution and Information Processing
IS - 4
M1 - 2250008
ER -