Reconstruction of vector (signal) by the norms of projections

Abstract

The foundations of the frame theory in finite-dimensional Euclidean space are represented. The ability of frames in the reconstruction of the vector signal without phase measurements are shown. There is a review of a number of new concepts and their role in the signal reconstruction. The possibility of reconstruction of the vector by the norms of the projections on the subspaces is asserted. Particular attention is paid to systems of subspaces for which there is the possibility of reconstruction by the norms of the projections on them and on their orthogonal complements.