TY - GEN
T1 - Biorthogonal bases of compactly supported matrix valued wavelets
AU - Slavakis, Konstantinos
AU - Yamada, Isao
PY - 1999/1/1
Y1 - 1999/1/1
N2 - We introduce the concept of biorthogonal bases of compactly supported matrix valued wavelets and examine the feasibility of their construction. Initially, we assume matrix filter banks assembled by FIR filters such that the perfect reconstruction property for matrix valued signals holds. Without admitting commutativity of any matrix multiplications and by imposing further conditions on the lowpass parts of the matrix filter banks, we construct compactly supported matrix valued wavelet functions that constitute biorthogonal Riesz bases for the matrix valued L2/(R, CN times/N/) signal space. To validate our design, we provide a class of biorthogonal compactly supported matrix valued wavelet bases. As a special case, a class of orthonormal compactly supported matrix valued wavelets is also constructed, which in turn leads to regular multiwavelet functions that possess symmetry, compact support and orthogonality properties.
AB - We introduce the concept of biorthogonal bases of compactly supported matrix valued wavelets and examine the feasibility of their construction. Initially, we assume matrix filter banks assembled by FIR filters such that the perfect reconstruction property for matrix valued signals holds. Without admitting commutativity of any matrix multiplications and by imposing further conditions on the lowpass parts of the matrix filter banks, we construct compactly supported matrix valued wavelet functions that constitute biorthogonal Riesz bases for the matrix valued L2/(R, CN times/N/) signal space. To validate our design, we provide a class of biorthogonal compactly supported matrix valued wavelet bases. As a special case, a class of orthonormal compactly supported matrix valued wavelets is also constructed, which in turn leads to regular multiwavelet functions that possess symmetry, compact support and orthogonality properties.
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U2 - 10.1109/ISSPA.1999.815836
DO - 10.1109/ISSPA.1999.815836
M3 - Conference contribution
AN - SCOPUS:0004543312
SN - 1864354518
SN - 9781864354515
T3 - ISSPA 1999 - Proceedings of the 5th International Symposium on Signal Processing and Its Applications
SP - 981
EP - 985
BT - ISSPA 1999 - Proceedings of the 5th International Symposium on Signal Processing and Its Applications
PB - IEEE Computer Society
T2 - 5th International Symposium on Signal Processing and Its Applications, ISSPA 1999
Y2 - 22 August 1999 through 25 August 1999
ER -