Iterations of the generalized Gram-Schmidt procedure for generating Parseval frames

In this paper we describe some properties of the generalized Gram-Schmidt procedure (GGSP) for generating Parseval frames which was first introduced by Casazza and Kutyniok [A generalization of Gram-Schmidt orthogonalization generating all Parseval frames, Adv. Comput. Math. 27 (2007), pp. 65-78]. Next we investigate the iterations of the procedure and its limit. In the end we give some examples of the iterated procedure.Comment: 10 pages, 3 figure

Optimal Dual Frames For Erasures And Discrete Gabor Frames

Since their discovery in the early 1950\u27s, frames have emerged as an important tool in areas such as signal processing, image processing, data compression and sampling theory, just to name a few. Our purpose of this dissertation is to investigate dual frames and the ability to find dual frames which are optimal when coping with the problem of erasures in data transmission. In addition, we study a special class of frames which exhibit algebraic structure, discrete Gabor frames. Much work has been done in the study of discrete Gabor frames in Rn, but very little is known about the l2(Z) case or the l2(Zd) case. We establish some basic Gabor frame theory for l2(Z) and then generalize to the l2(Zd) case

Iterations of the generalized Gram-Schmidt procedure for generating Parseval frames

In this paper we describe some properties of the generalized Gram–Schmidt procedure (GGSP) for generating Parseval frames which was first introduced in [3]. Next we investigate the iterations of the procedure and its limit. In the end we give some examples of the iterated procedure