Complemented block bases of symmetric bases and spectral tetris fusion frame constructions

2012 ◽  
Author(s):  
Andreas Heinecke
Keyword(s):  
Fusion Frame ◽  
Symmetric Bases ◽  
Spectral Tetris

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

scholarly journals Weighted fusion frame construction via spectral tetris

2013 ◽  
Vol 40 (2) ◽  
pp. 335-351 ◽  
Author(s):  
Peter G. Casazza ◽  
Jesse Peterson
Keyword(s):  
Fusion Frame ◽  
Weighted Fusion ◽  
Spectral Tetris ◽  
Frame Construction

scholarly journals Spectral Tetris Fusion Frame Constructions

2012 ◽  
Vol 18 (4) ◽  
pp. 828-851 ◽  
Author(s):  
Peter G. Casazza ◽  
Matthew Fickus ◽  
Andreas Heinecke ◽  
Yang Wang ◽  
Zhengfang Zhou
Keyword(s):  
Fusion Frame ◽  
Spectral Tetris

Symmetric Bases

1996 ◽  
pp. 113-136
Author(s):  
Joram Lindenstrauss ◽  
Lior Tzafriri
Keyword(s):  
Symmetric Bases

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.

Sign in / Sign up

Export Citation Format

Share Document