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On the relation of the frame-related operators of fusion frame systems [PDF]
Sampling Theory, Signal Processing, and Data Analysis, 2023 AbstractFrames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed processing techniques, which naturally leads to the concept of fusion frames and fusion frame systems.
Lukas Köhldorfer +2 more
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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
exaly +4 more sources
Sahand Communications in Mathematical AnalysisIn this papaer, we introduce fuzzy fusion frame and express related operators. Also, we explain some properties of fuzzy fusion frame and fusion fuzzy Bessel family, and we bring the representive of fuzzy fusion frame, the fuzzy Parseval fusion frame.
Bayaz Daraby, Vahid Ebrahimi
doaj +2 more sources
Construction of continuous $g$-frames and continuous fusion frames [PDF]
Sahand Communications in Mathematical Analysis, 2016 A generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by M. H. Faroughi and R. Ahmadi, is presented in this study. Continuous resolution of the identity (CRI) is introduced, a new family of
Mahdiyeh Khayyami, Akbar Nazari
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3D Road Defect Mapping via Differentiable Neural Rendering and Multi-Frame Semantic Fusion in Bird’s-Eye-View Space [PDF]
Journal of ImagingRoad defect detection is essential for traffic safety and infrastructure maintenance. Excising automated methods based on 2D image analysis lack spatial context and cannot provide accurate 3D localization required for maintenance planning.
Hongjia Xing, Feng Yang
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A Note on Some Results for $C$-controlled $K$-Fusion Frames in Hilbert Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this manuscript, we study the relation between K-fusion frame and its local components which leads to the definition of a $C$-controlled $K$-fusion frames, also we extend a theory based on K-fusion frames on Hilbert spaces, which prepares exactly the ...
Habib Shakoory +3 more
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Woven g-Fusion Frames in Hilbert Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this paper, we introduce the notion of woven g-fusion frames in Hilbert spaces. Then, we present sufficient conditions for woven g-fusion frames in terms of woven frames in Hilbert spaces.
Maryam Mohammadrezaee +3 more
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Generalized atomic subspaces for operators in Hilbert spaces [PDF]
Mathematica Bohemica, 2022 We introduce the notion of a $g$-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of $g$-fusion frames.
Prasenjit Ghosh, Tapas Kumar Samanta
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Continuous $k$-Fusion Frames in Hilbert Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2020 The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for
Vahid Sadri +3 more
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