Results 11 to 20 of about 86,530 (254)
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
Ana Benavente
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Journal of Mathematical Analysis and Applications, 2008 The authors study generalized, i.e., \(g\)-frames in a Hilbert space \(U\), that is, sequences \((\Lambda_i)_{i\in I}\) of linear operators \(\Lambda_i:U\to V_i\) such that \[ A\| f\| ^2 \leq \sum_{i\in I} \| \Lambda_i f\| ^2 \leq B \| f\| ^2, \] for some positive constants \(A\) and \(B\).
Amir Khosravi
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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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Non-orthogonal Fusion Frames and the Sparsity of Fusion Frame Operators [PDF]
Journal of Fourier Analysis and Applications, 2011 Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator $S_{\cW}$, which in turn is heavily dependent on ...
Jameson Cahill +2 more
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Some equalities and inequalities for fusion frames. [PDF]
Springerplus, 2016 Fusion frames have some properties similar to those of frames in Hilbert spaces, but not all of their properties are similar. Some authors have established some equalities and inequalities for conventional frames. In this paper, we give some equalities and inequalities for fusion frames.
Guo Q, Leng J, Li H.
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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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Filter Bank Fusion Frames [PDF]
IEEE Transactions on Signal Processing, 2011 In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly designed, fusion frames can provide redundant encodings of signals which are optimally robust against certain types of
Matthew Fickus, Dustin G Mixon
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Fusion frames and G-frames in Banach spaces
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amir Khosravi +2 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 G Casazza, Shidong Li
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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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