A generalization of Gram-Schmidt orthogonalization generating all Parseval frames

Frames have turned out to be an essential tool for many applications such as, for example, data transmission, due to their robustness not only against noise but also against losses and due to their freedom in design [4, 6]. Their main advantage lies in the fact that a frame can be designed to be redundant while still providing a reconstruction formula. Since the frame operator Sg = ∑n i=1 〈g, fi〉 fi is invertible, each vector g ∈ H can be always reconstructed from the values (〈g, fi〉)i=1 via g = SSg = n