Tight frame approximation for multi-frames and super-frames Original Research Article

We consider a generator Φ=(φ1, … ,φN) 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 Ψ=(ψ1,…,ψN) such that ∑j=1N||φj−ψj||2⩽∑j=1N||φj−ψj||2 holds for all the normalized tight multi-frame (resp. super-frame) generators η=(η1,…,ηN). We also investigate the similar problems for dual frames and discuss a few applications to Gabor frames and some other frames.