Optimal Dual Frames for Probabilistic Erasures

Assume that a frame is given for encoding in a communication system. J. Leng
et al.
investigated its dual frames for signal decoding which minimize the maximal error when the probabilistic erasures occur in the transmission process. In this paper, we present a new sufficient condition such that the canonical dual is the unique probability optimal dual for erasures. The determination conditions in our results reduces the computational complexity. We also give a necessary and sufficient condition under which a kind of alternative dual frames are probability optimal dual, and study the relation between the optimal duals of equivalent frames. Moreover, we present several examples which show that the general optimal dual frame is not a probability optimal dual frame and compare the reconstruction effects when the general optimal dual frames, the new probability optimal, and the existing probability optimal dual frames are used for decoding.