Duality for matrix-valued wave packet frames in L2(ℝd, ℂs×r)

Abstract

Dual frames are generalized Riesz bases which have potential applications in signal processing. In this paper, the construction of dual frames of matrix-valued wave packet systems in the matrix-valued function space [Formula: see text] from dual pairs of atomic wave packet frames in [Formula: see text] is studied. A class of matrix-valued dual generators from its associated dual pair of atomic wave packets has been obtained. We provide a characterization of matrix-valued dual window functions in terms of orthogonality of wave packet Bessel sequences. A perturbation result with respect to window functions for matrix-valued dual frames is given. It is well known that an orthogonal Parseval Hilbert frame for a Hilbert space turned out be an orthonormal basis for the space, however, this is not true for an orthogonal matrix-valued wave packet Parseval frame for the underlying matrix-valued function space. We give a type of matrix-valued orthonormal basis associated with an orthonormal basis of [Formula: see text].