Probability modelled optimal frames for erasures

We establish a probability model for constructing optimal Parseval frames when erasures occur during the transmission process of the frame coefficient data set. Such frames are called probability modelled (PM) optimal frames for erasures. While (PM) optimal frames exist for all erasures, it is usually difficult to construct them. We characterize all the PM optimal frames for one and two erasures, and propose an algorithm to construct these frames. Examples are given to demonstrate the construction and to compare the decoding/reconstruction effects when both PM optimal Parseval frames and uniform length Parseval frames are used for encoding.