The invertibility of fusion frame multipliers

Shamsabadi, Mitra; Arefijamaal, Ali Akbar

doi:10.1080/03081087.2016.1228803

Cited by 18 publications

(13 citation statements)

References 12 publications

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“…Since their introduction in 2007 (see [4]), ordinary Bessel multipliers, as a generalization of Gabor multipliers [12], have been extensively generalized and studied, see for example [3,5,17,18,24]. The reader will remark that invertible Bessel multipliers is a proper generalization of duality notion in Hilbert spaces which permits us to have different reconstruction strategies.…”

Section: Resultsmentioning

confidence: 99%

“…The reader will remark that invertible Bessel multipliers is a proper generalization of duality notion in Hilbert spaces which permits us to have different reconstruction strategies. However, there has only been one approach yet for studying the invertibility of fusion frame multipliers [24]. In the following, we want to study a new concept of Bessel fusion multipliers in Hilbert spaces, which is a slightly modified version of [3,24].…”

Section: Resultsmentioning

confidence: 99%

“…This notion of duality for fusion frame in the sense of [22], as the main object of study of this work, will be explained and justified in the next sections. Moreover, based on this duality notion for fusion frames, we propose a new concept of Bessel fusion multipliers in Hilbert spaces, which is a slightly modified version of [3,24]. It extends the commonly used notion and, in particular, we show that with this definition in many cases Bessel fusion multipliers behave similar to ordinary Bessel multipliers.…”

Section: Introductionmentioning

confidence: 82%

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Dual fusion frames in the sense of Kutyniok, Paternostro and Philipp with applications to invertible Bessel fusion multipliers

Javanshiri¹,

Fattahi²,

Sargazi³

2018

Preprint

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To achieve our main research goal, first we survey the approaches towards dual fusion frames existing in the literature and agree on the notion of duality for fusion frames in the sense of Kutyniok, Paternostro and Philipp (Oper. Matrices 11 (2017), no. 2, 301-336). As a main result we show that different fusion frames have different dual fusion frames. Moreover, this duality notion leads to a new definition of Bessel fusion multipliers which is a slightly modified version of the commonly used definitions. Particularly, we show that with this definition in many cases Bessel fusion multipliers behave similar to ordinary Bessel multipliers. Finally, special attention is devoted to the study of dual fusion frames induced by an invertible Bessel fusion multiplier.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 82%

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Dual fusion frames in the sense of Kutyniok, Paternostro and Philipp with applications to invertible Bessel fusion multipliers

Javanshiri¹,

Fattahi²,

Sargazi³

2018

Preprint

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“…Recently, due to application and theoretical goals, some generalizations of frames have been presented, such as g-frames [22], K-frames [18] and fusion frames [11,21]. In most of them and many application problems, reconstruction and duality play a key role.…”

Section: Introductionmentioning

confidence: 99%

On Excesses and Duality in Woven Frames

Moghaddam¹,

Arefijamaal²

2021

Preprint

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Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. In this paper, we study the notion of excess for woven frames and prove that any two frames in a separable Hilbert space that are woven have the same excess. We also show that every frame with a large class of duals is woven provided that its redundant elements have small enough norm. Also, we try to transfer the woven property from frames to their duals and vise versa. Finally, we look at which perturbations of dual frames preserve the woven property, moreover it is shown that under some conditions the canonical Pareseval frame of two woven frames are also woven.

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“…Frame multipliers have many applications in psychoacoustical modeling and denoising [6,24]. Moreover, several generalizations of multipliers are proposed [5,21,22].…”

Section: Introduction Notation and Motivationmentioning

confidence: 99%

Some Results of K-Frames and Their Multipliers

2020

Turk J Math

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The invertibility of fusion frame multipliers

Cited by 18 publications

References 12 publications

Dual fusion frames in the sense of Kutyniok, Paternostro and Philipp with applications to invertible Bessel fusion multipliers

Dual fusion frames in the sense of Kutyniok, Paternostro and Philipp with applications to invertible Bessel fusion multipliers

On Excesses and Duality in Woven Frames

Some Results of K-Frames and Their Multipliers

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