  Comparing with univariate framelets, the main challenge involved in studying
multivariate framelets is that we have to deal with the highly non-trivial
problem of factorizing multivariate polynomial matrices. As a consequence,
multivariate framelets are much less studied than univariate framelets in the
literature. Among existing works on multivariate framelets, multivariate
multiframelets are much less considered comparing with the exitensively studied
scalar framelets. Hence multiframelets are far from being well understood. In
this paper, we focus on multivariate dual multiframelets (or dual vector
framelets) obtained through the popular oblique extension principle (OEP),
which are called OEP-based dual multiframelets. We will show that from any
given pair of compactly supported refinable vector functions, one can always
construct an OEP-based dual mltiframelet, such that its generators have the
highest possible order of vanishing moments. Moreover, the associated discrete
framelet transform is compact and sparse.
