Balanced Multiwavelets With Interpolatory Property

Abstract

Balanced multiwavelets with interpolatory property are discussed in this paper. This kind of multiwavelets can have a sampling property like Shannon's sampling theorem. It has been shown that the corresponding matrix-valued refinable mask has special structure, and an orthogonal multifilter bank {H(z),G(z)} can be reduced to a scalar valued conjugate quadrature filter (CQF) a(z) . But it does not mean that any scalar CQF can form a "good" multifilter bank which can generate a vector-valued refinable function with some degree of smoothness. In the context of balanced multiwavelets, we give the definition of transferring balance order, which a scalar CQF a(z) satisfies, to guarantee that the multiwavelet Ψ generated is balanced. On the basis of the parametrization of a scalar CQF with any length and conditions of transferring balance order, parametrization of multifilter banks which can generate interpolatory multiwavelet and interpolatory scaling function, is gotten. Moreover, some balanced interpolatory multiwavelets have been constructed. Interpolatory analysis-ready multiwavelets (armlets) are also discussed in this paper. It is known that conditions of armlets are easy to validate, compared with balanced multiwavelets. But it will be present that if the corresponding scaling function Φ is interpolatory, the multiwavelet Ψ is balanced of order n if and only if it is an armlet of order n. Finally, the application of balanced multiwavelets with interpolatory property in image processing is also discussed.