Spectral tetris fusion frame constructions

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.

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Nonuniform recovery of fusion frame structured sparse signals

Analysis and Applications ◽

10.1142/s0219530516500032 ◽

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].

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

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691308002458 ◽

2008 ◽

Vol 06 (03) ◽

pp. 433-446 ◽

Cited By ~ 20

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.

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C-Fusion Frame

Journal of Applied Sciences ◽

10.3923/jas.2008.2881.2887 ◽

2008 ◽

Vol 8 (16) ◽

pp. 2881-2887 ◽

Cited By ~ 4

Author(s):

M.H. Faroughi ◽

R. Ahmadi

Keyword(s):

Fusion Frame

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Controlled g-fusion frame in Hilbert space

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691321500090 ◽

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.

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