Weighted and controlled frames

Details Weighted and controlled frames Weighted and controlled frames

2006-11-23

arxiv.org/abs/math/0611729v2

International Journal of Wavelets, Multiresolution and Information Processing, Volume 8 (1), pp. 109-132, 2010

Mathematics

Functional Analysis

21 pages, 5 figures; Added one author (Grybos), cut some parts, added numerical experiments

Scientific paper

10.1142/S0219691310003377

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while offering a numerical advantage in the sense of preconditioning. Next, we investigate weighted frames, in particular their relation to controlled frames. We consider the special case of semi-normalized weights, where the concepts of weighted frames and standard frames are interchangeable. We also make the connection with frame multipliers. Finally we analyze weighted frames numerically. First we investigate three possibilities for finding weights in order to tighten a given frame, i.e., decrease the frame bound ratio. Then we examine Gabor frames and how well the canonical dual of a weighted frame is approximated by the inversely weighted dual frame.

Affiliated with

Also associated with

No associations

Rating

Weighted and controlled frames does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weighted and controlled frames, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weighted and controlled frames will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-700701