Tight frame approximation for multi-frames and super-frames
Abbreviated Journal Title
J. Approx. Theory
frames; projective unitary systems; multi-fraines and super-frames; approximation; approximation; Gabor frames; shift-invariant subspaces; WEYL-HEISENBERG FRAMES; GABOR FRAMES; BASES; Mathematics
We consider a generator Phi = (phi(1),...,phi(N)) for either a multi-frame or a super-frame generated under the action of a projective unitary representation for a discrete countable group. Examples of such frames include Gabor multi-frames, Gabor super-frames and frames for shift-invariant subspaces. We show that there exists a unique normalized tight multi-frame (resp. super-frame) generator Psi = (psi(1),..,psi(N)) such that Sigma(j=1)(N)\\phi(J) - psi(j)\\(2) less than or equal to Sigma(j=1)(N)\\phi(j) - psi(j)\\(2) holds for all the normalized tight multi-frame (resp. super-frame) generators eta = (eta(1),...,eta(N)). We also investigate the similar problems for dual frames and discuss a few applications to Gabor frames and some other frames. (C) 2004 Elsevier Inc. All rights reserved.
Journal of Approximation Theory
"Tight frame approximation for multi-frames and super-frames" (2004). Faculty Bibliography 2000s. 4404.