Oblique Dual Fusion Frames. (19th May 2018)

• Record Type: Journal Article
• Authors: Heineken, Sigrid B.; Morillas, Patricia M.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 7(2018)
• Page Start: 800
• Page End: 824
• Publication Date: 2018-05-19
• Subjects: Consistent reconstruction -- frames -- fusion frames -- oblique dual frames -- oblique dual fusion frames -- oblique projections; Primary 42C15 -- Secondary 42C40, 46C05, 47A05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1421555
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals considered as elements in a Hilbert space are, under certain requirements, analyzed in one subspace and reconstructed in another subspace. The requirements are, on one side, the uniqueness of the reconstructed signal, and on the other what we call consistency of the sampling for fusion frames. Both conditions are naturally related to oblique projections. We study the main properties of oblique dual fusion frames and oblique dual fusion frame systems introduced in this work and present several results that provide alternative methods for their construction.