A Class of Parseval Fusion Frames for Probabilistic Erasures

Abstract

The fusion frame, as a generated frame, has a wide range of applications in engineering. In the data erasures problem, for any fusion frame, trying to find its optimal dual fusion frame is an important problem. In our paper we plan to discuss the problem of probabilistic erasures by using the probabilistic model. We construct a fusion frame {W, w} such that its dual fusion frame {W, v} is the unique probability optimal dual frames in some cases. Such fusion frame is called probability uniform Parseval fusion frame. We discuss the existence of the probability uniform Parseval fusion frame and the applications of probability uniform Parseval fusion frame. Then we get the relationship of probability uniform Parseval fusion frame and their optimal dual fusion frame. And then we can see the advantage of probability uniform Parseval fusion frame from some properties.