A New Look at Optimal Dual Problem Related to Fusion Frames

Abstract

The purpose of this work is to examine the structure of optimal (alternate) dual fusion frames and get more flexibility in the use of (alternate) dual fusion frames for erasures of subspaces. We deal with optimal alternate dual fusion frames with respect to different definitions of duality. We compare the advantages of alternate and component preserving dual fusion frames. Then, we further study optimal alternate dual fusion frames. We also introduce a new concept of the so-called partial optimal dual which involves less computations for detecting optimal dual for erasures in known locations. Then we study the relationship between local and global optimal duals by partial optimal duals which leads to some applicable results. In the sense that, we obtain an overcomplete frame and a family of associated optimal duals by a given Riesz fusion basis. We present some examples to exhibit the effect of error rate when alternate dual fusion frames are applied in reconstruction.