Probabilistic Modelled Optimal Frame for Erasures under Spectral and Operator Norm

Abstract

Error occurs in data transmission process when some data are missing at the time of reconstruction. Finding the best dual frame or a dual pair that minimizes the reconstruction error when erasure occurs,is a deep-rooted problem in frame theory. The main motivation behind this paper is to characterize the optimal dual under the spectral and operator norms. Here we give several equivalent conditions for which the canonical dual is an optimal dual frame for a given frame. We also go on to characterize the set of dual pairs which attains the optimal value.