1 Applied functional analysis, Department of Mathematics, Technical University of Denmark2 Department of Mathematics, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark4 unknown
Given a frame for a subspace W of a Hilbert space H, we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace V. In place of the standard description, which involves computing the pseudoinverse of the frame operator, we develop an alternative characterization which in some cases can be computationally more efficient. We first treat the case of a general frame on an arbitrary Hilbert space, and then specialize the results to shift-invariant frames with multiple generators. In particular, we present explicit versions of our general conditions for the case of shift-invariant spaces with a single generator. The theory is also adapted to the standard frame setting in which the original and dual frames are defined on the same space. Copyright (C) 2006 Hindawi Publishing Corporation. All rights reserved.
Eurasip Journal on Applied Signal Processing, 2006, p. 1-11