loading page

A SURVEY ON PHASE RETRIEVAL AND NORM RETRIEVAL IN HILBERT SPACES
  • SAIKAT MUKHERJEE,
  • SUMAN DOWERAH
SAIKAT MUKHERJEE
National Institute of Technology Meghalaya

Corresponding Author:saikat.mukherjee@nitm.ac.in

Author Profile
SUMAN DOWERAH
National Institute of Technology Meghalaya
Author Profile

Abstract

One of the crucial and major issues in engineering, particularly in signal processing, is signal reconstruction. Frames are flexible tools that helps to reconstruct signals/vectors in a stable way. Frame theory was introduced for Hilbert spaces by Duffin et al. in 1952. If it happens that we only have the intensity measurements or the phaseless measurements of the lost signal then reconstructing the original signal becomes difficult. In such cases, phase retrieval sequences play essential roles to reconstruct or regain the signal from its intensity measurements or phaseless measurements. In 2006, Balan et al. introduced phase retrievable frames for Hilbert spaces. Phase retrieval has received significant attention in various fields, including image processing and signal reconstruction. Similar to phase retrieval, norm retrieval sequences help to regain the norm of the original signal. In 2015 Bahmanpour et al. introduced norm retrieval sequences for Hilbert spaces. We provide a thorough overview of phase retrieval and norm retrieval by vectors and subspaces in separable Hilbert space. We also highlight and discuss the recent developments in phase retrieval and norm retrieval of partially lost signals.
06 Feb 2024Reviewer(s) Assigned
14 Mar 2024Review(s) Completed, Editorial Evaluation Pending
06 May 2024Submission Checks Completed
06 May 2024Assigned to Editor
20 Jun 2024Review(s) Completed, Editorial Evaluation Pending