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The Structure of Minimizers of the Frame Potential on Fusion Frames [PDF]
Journal of Fourier Analysis and Applications, 2009 In this paper we study the fusion frame potential, that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. The structure of local and global minimizers of this potential is studied, when we restrict the frame potential to suitable sets of fusion frames. These minimizers are related to
Pedro Massey +2 more
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Archiv Der Mathematik, 2014 The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogous to the canonical dual frame. Here a new concept of dual is studied in infinite-dimensional separable Hilbert spaces. It extends the commonly used notion and overcomes these technical difficulties. We
Heineken, Sigrid Bettina +3 more
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Fusion frames and distributed processing
Applied and Computational Harmonic Analysis, 2008 Let $\{W_i\}_{i\in I}$ be a (redundant) sequence of subspaces each being endowed with a weight $v_i$, and let $\mathcal{H}$ be the closed linear span of the $W_i$'s, a composite Hilbert space. Provided that $\{(W_i,v_i)\}_{i \in I}$ satisfies a certain property which controls the weighted overlaps of the subspaces, it is called a {\em fusion frame ...
Peter Casazza, Gitta Kutyniok
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2021
Summary: In this paper, we show that fusion frames in the finite dimensional Hilbert space \(H\) correspond to frames in the Hilbert \(C^\ast\)-module \(\mathcal{B}\left(\mathbb{C}^n\right)\). Moreover, we show that every tight fusion frame and Riesz fusion basis in \(\mathbb{C}^n\) correspond to a tight frame and Riesz basis in the Hilbert \(C^\ast ...
Kamyabi-Gol, Rajab Ali +1 more
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Summary: In this paper, we show that fusion frames in the finite dimensional Hilbert space \(H\) correspond to frames in the Hilbert \(C^\ast\)-module \(\mathcal{B}\left(\mathbb{C}^n\right)\). Moreover, we show that every tight fusion frame and Riesz fusion basis in \(\mathbb{C}^n\) correspond to a tight frame and Riesz basis in the Hilbert \(C^\ast ...
Kamyabi-Gol, Rajab Ali +1 more
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Applied and Computational Harmonic Analysis, 2013 Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion frames. Tight p-fusion frames are closely related to the classical notions of designs and cubature formulas in Grassmann spaces and are analyzed with methods from harmonic ...
Bachoc, Christine, Ehler, Martin
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New characterizations of fusion frames (frames of subspaces)
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2009 This work gives new characterizations of fusion frames, studies the behavior of fusion frames under bounded operators with closed range, and erasures of subspaces of fusion frames. It also shows that every fusion frame is the image of an orthonormal fusion basis under a bounded surjective operator.
Mohammad Sadegh Asgari
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Oblique Dual Fusion Frames [PDF]
Numerical Functional Analysis and Optimization, 2018 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 and under certain consistency requirements, are analyzed in one subspace and are reconstructed in another subspace.
Heineken, Sigrid Bettina +1 more
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On the stability of fusion frames (frames of subspaces)
Acta Mathematica Scientia, 2011Abstract A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame (frame of subspaces) is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces.
Mohammad Sadegh Asgari
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Semi-frames and Fusion Semi-frames
2018This paper is a short survey of the theory of semi-frames and fusion semi-frames in Hilbert and Banach spaces.
Nabin Kumar Sahu, Ram N. Mohapatra
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Weaving g-Frames and Weaving Fusion Frames
Bulletin of the Malaysian Mathematical Sciences Society, 2018The authors study weaving \(g\)-frames and weaving fusion frames. The authors also show that they are stable under invertible operators and small perturbations. In addition woven \(g\)-frames and weakly woven \(g\)-frames coincide.
Khosravi, Amir +1 more
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