Norm retrieval by vectors and projections

Abstract

Norm retrieval was introduced for Hilbert space frames for the first time by Bahmanpour et. al. in the year 2015. In order for a subspace as well as its orthogonal complement to do norm retrieval, it was proved by Bahmanpour et. al. that norm retrieval is a necessary requirement. Basically, norm retrieval refers to the process of reconstructing the signal’s norm from the intensity measurements. We give a few characterizations for norm retrieval by vectors and subspaces under the action of bounded linear operators.