Gabor Tight Fusion Frames: Construction and Applications in Signal Retrieval Modulo Phase

TL;DR

This paper introduces a novel method for constructing non-trivial tight fusion frames using Gabor analysis and demonstrates their usefulness in phase-modulo signal retrieval.

Contribution

It presents the first non-trivial construction of tight fusion frames and explores their application in phase-modulo signal retrieval.

Findings

Successfully constructed non-trivial tight fusion frames using Gabor analysis

Demonstrated the application of these frames in signal retrieval modulo phase

Provided theoretical foundations for future research in fusion frame applications

Abstract

Hilbert space fusion frames are a natural extension of Hilbert space frames, extending the notion from a set of vectors in a Hilbert space to a set of subspaces of a Hilbert space with analogous notions of overcompleteness and boundedness. As tight frames are a very important topic within standard frame theory, tight fusion frames are similarly important; however, only trivial examples of tight fusion frames are hitherto known. In this paper, we apply ideas from Gabor analysis to demonstrate a non-trivial construction of tight fusion frames. We then use this construction to further show their applicability in some cases for the retrieval of signals modulo phase.