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.

UR - http://www.scopus.com/inward/record.url?scp=0004543312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004543312&partnerID=8YFLogxK

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 -