arXiv subjects

Fahimeh Arabyani-Neyshaburi

Publications and source records attributed to Fahimeh Arabyani-Neyshaburi.

3 recordsLinked to original sources

arXiv2025

Continuous Approach to Phase (Norm) Retrieval Frames

This paper investigates the properties of continuous frames, with a particular focus on phase retrieval and norm retrieval in the context of Hilbert spaces. We introduce the concept of continuous near-Riesz bases and prove their invariance under invertible operators. Some equivalent conditions for phase and norm retrieval property of continuous frames are presented. We study the stability of phase retrieval under perturbations. Furthermore, tensor product frames for separable Hilbert spaces are studied, and we establish the equivalence of phase retrieval and norm retrieval properties between components and their tensor products.

math.FA↗

arXiv2023

Characterization of (weak) phase retrieval dual frames

Recovering a signal up to a unimodular constant from the magnitudes of linear measurements has been popular and well studied in recent years. However, numerous unsolved problems regarding phase retrieval still exist. Given a phase retrieval frame, may the family of phase retrieval dual frames be classified? And is such a family dense in the set of dual frames? Can we present the equivalent conditions for a family of vectors to do weak phase retrieval in complex Hilbert space case? What is the connection between phase, weak phase and norm retrieval? In this context, we aim to deal with these open problems concerning phase retrieval dual frames, weak phase retrieval frames, and specially investigate equivalent conditions for identifying these features. We provide some characterizations of alternate dual frames of a phase retrieval frame which yield phase retrieval in finite dimensional Hilbert spaces. Moreover, for some classes of frames, we show that the family of phase retrieval dual frames is open and dense in the set of dual frames. Then, we study weak phase retrieval problem. Among other things, we obtain some equivalent conditions on a family of vectors to do phase retrieval in terms of weak phase retrieval.

math.FA↗

arXiv2021

A New Look at Optimal Dual Problem Related to Fusion Frames

The purpose of this work is to examine the structure of optimal dual fusion frames and get more exibility in the use of dual fusion frames for erasures of subspaces. We deal with optimal dual fusion frames with respect to different definitions of duality and compare the advantages of these approaches. In addition, we introduce a new concept so called partial optimal dual which involves less time and computation 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 dual fusion frames are applied in reconstruction.

math.FA↗