scholarly journals Local sparsity and recovery of fusion frame structured signals

2020 ◽  
Vol 174 ◽  
pp. 107615
Author(s):  
Roza Aceska ◽  
Jean-Luc Bouchot ◽  
Shidong Li
Keyword(s):  
Fusion Frame

Construction of g-fusion frames in Hilbert spaces

2020 ◽  
Vol 23 (02) ◽  
pp. 2050015
Author(s):  
Vahid Sadri ◽  
Gholamreza Rahimlou ◽  
Reza Ahmadi ◽  
Ramazan Zarghami Farfar
Keyword(s):  
Hilbert Spaces ◽  
Closed Range ◽  
Fusion Frames ◽  
Interesting Topic ◽  
Fusion Frame

After introducing g-frames and fusion frames by Sun and Casazza, respectively, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give characterizations of these frames from the viewpoint of closed range and g-fusion frame sequences. Also, the canonical dual g-fusion frames are presented and we introduce a Parseval g-fusion frame.

Nonuniform recovery of fusion frame structured sparse signals

2017 ◽  
Vol 15 (03) ◽  
pp. 333-352
Author(s):  
Yu Xia ◽  
Song Li
Keyword(s):  
Probability Distribution ◽  
Compressed Sensing ◽  
Fourier Coefficients ◽  
A Priori ◽  
Sparse Recovery ◽  
A Priori Knowledge ◽  
Sparse Signals ◽  
Fusion Frame ◽  
Redundant Representation ◽  
Vector Valued

This paper considers the nonuniform sparse recovery of block signals in a fusion frame, which is a collection of subspaces that provides redundant representation of signal spaces. Combined with specific fusion frame, the sensing mechanism selects block-vector-valued measurements independently at random from a probability distribution [Formula: see text]. If the probability distribution [Formula: see text] obeys a simple incoherence property and an isotropy property, we can faithfully recover approximately block sparse signals via mixed [Formula: see text]-minimization in ways similar to Compressed Sensing. The number of measurements is significantly reduced by a priori knowledge of a certain incoherence parameter [Formula: see text] associated with the angles between the fusion frame subspaces. As an example, the paper shows that an [Formula: see text]-sparse block signal can be exactly recovered from about [Formula: see text] Fourier coefficients combined with fusion frame [Formula: see text], where [Formula: see text].

FUSION FRAMES AND g-FRAMES IN HILBERT C*-MODULES

2008 ◽  
Vol 06 (03) ◽  
pp. 433-446 ◽  
Author(s):  
AMIR KHOSRAVI ◽  
BEHROOZ KHOSRAVI
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Hilbert Spaces ◽  
Frame Theory ◽  
Fusion Frames ◽  
Perturbation Result ◽  
Fusion Frame

The notion of frame has some generalizations such as frames of subspaces, fusion frames and g-frames. In this paper, we introduce fusion frames and g-frames in Hilbert C*-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. We also generalize a perturbation result in frame theory to g-frames in Hilbert spaces. We also show that tensor product of fusion frames (g-frames) is a fusion frame (g-frame) and tensor product of resolution of identity is a resolution of identity.

C-Fusion Frame

2008 ◽  
Vol 8 (16) ◽  
pp. 2881-2887 ◽  
Author(s):  
M.H. Faroughi ◽  
R. Ahmadi
Keyword(s):  
Fusion Frame

scholarly journals Spectral tetris fusion frame constructions

2011 ◽  
Author(s):  
Peter G. Casazza ◽  
Matthew Fickus ◽  
Andreas Heinecke ◽  
Yang Wang ◽  
Zhengfang Zhou
Keyword(s):  
Fusion Frame ◽  
Spectral Tetris

Controlled g-fusion frame in Hilbert space

2021 ◽  
pp. 2150009
Author(s):  
Hanbing Liu ◽  
Yongdong Huang ◽  
Fengjuan Zhu
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Iterative Algorithms ◽  
Bessel Sequence ◽  
Numerical Efficiency ◽  
Fusion Frames ◽  
Controlled Fusion ◽  
Fusion Frame

Fusion frame is a generalization of frame, which can analyze signals by projecting them onto multidimensional subspaces. Controlled fusion frame as generalization of fusion frame, it can improve the numerical efficiency of iterative algorithms for inverting the fusion frame operators. In this paper, we first introduce the notion of controlled g-fusion frame, discuss several properties of controlled g-fusion Bessel sequence. Then, we present some sufficient conditions and some characterizations of controlled g-fusion frames. Finally, we study the sum of controlled g-fusion frames.

scholarly journals Sparse Recovery From Combined Fusion Frame Measurements

2011 ◽  
Vol 57 (6) ◽  
pp. 3864-3876 ◽  
Author(s):  
Petros Boufounos ◽  
Gitta Kutyniok ◽  
Holger Rauhut
Keyword(s):  
Sparse Recovery ◽  
Fusion Frame

scholarly journals The Duals of Fusion Frames for Experimental Data Transmission Coding of High Energy Physics

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jinsong Leng ◽  
Qixun Guo ◽  
Tingzhu Huang
Keyword(s):  
Experimental Data ◽  
Data Transmission ◽  
High Energy Physics ◽  
Matrix Representation ◽  
High Energy ◽  
Fusion Frames ◽  
Fusion Frame ◽  
The Matrix ◽  
Frame System ◽  
Energy Physics

The experimental data transmission is an important part of high energy physics experiment. In this paper, we connect fusion frames with the experimental data transmission implement of high energy physics. And we research the utilization of fusion frames for data transmission coding which can enhance the transmission efficiency, robust against erasures, and so forth. For this application, we first characterize a class of alternate fusion frames which are duals of a given fusion frame in a Hilbert space. Then, we obtain the matrix representation of the fusion frame operator of a given fusion frame system in a finite-dimensional Hilbert space. By using the matrix representation, we provide an algorithm for constructing the dual fusion frame system with its local dual frames which can be used as data transmission coder in the high energy physics experiments. Finally, we present a simulation example of data coding to show the practicability and validity of our results.

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