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Keywords
(1)
riesz bases
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An introduction to frames and Riesz bases
An introduction to frames and Riesz bases,Ole Christensen
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An introduction to frames and Riesz bases
(
Citations: 491
)
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Ole Christensen
Published in 2003.
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Citation Context
(232)
...For the Parseval frames, the reconstruction formula holds true
12
37
...
S. Häuser
,
et al.
Convex multiclass segmentation with shearlet regularization
...Frame theory has applications to a wide variety of problems in signal processing and much more (see the monographs [
12
,
15
] for a comprehensive view)...
Bernhard G. Bodmann
,
et al.
Fusion Frames and the Restricted Isometry Property
...Frames were introduced by Duffin and Schaeffer in
2
, and have been developed very quickly in the past 20 more years, see
1
,
3
,
4
...
Zhijing Zhao
,
et al.
Sufficient conditions and stability of wavelet superframes
...This characterization may be viewed as the fusion frame counterpart to Naimark’s theorem [13, 17,
28
, 36], where Parseval frames are characterized as frame systems generated by an orthogonal projection of an orthonormal basis from a larger Hilbert space...
...[13,
28
, 36]) that there exists a Hilbert space K ⊃ H with an orthonormal basis {˜ eij}i∈I, j∈Ji so that the orthogonal projection P of K onto H satisfies...
...is a Parseval frame for H .B y [13,
28
, 36], there exists a Hilbert space K ⊇ H, an orthogonal projection P : K → H, and an orthonormal basis {eij}i∈I, j∈Ji for K so that...
Robert Calderbank
,
et al.
Sparse fusion frames: existence and construction
...It also encompasses a large class of signal representations commonly used in signal processing, including the Gabor and wavelet transforms [
16
]...
...the uniform timefrequency tiling in Gabor representations [
16
])...
...Examples include the translation, modulation, and dilatation operators, which are used, respectively, in classical shiftinvariant (SI) sampling problems [1], [2], in magnetic resonance imaging (MRI) and Gabor analysis [17], and in wavelet analysis [
16
], [18], [19]...
...Remark 1: The above theorem is well known for the case in which the sequence is generated by the translation operator given in Example 1 (see, e.g., [
16
], [19], [24], [34])...
...Consequently, the subset of past sampling functions cannot be a Riesz basis for the whole sampling space . However, it is still a Riesz basis for the past sampling space (see, e.g., [
16
]) so that causal processing can be pursued in a stable manner...
...and consequently it also cannot be a Riesz basis or a frame for (see, e.g., [
16
])...
...It remains to show that is a Bessel sequence, Riesz basis, or frame if the spectral density satisfies the conditions of Theorem 6. It is known (see, e.g., [
16
]) that is a Riesz basis for with Riesz bounds if and only if...
Tomer Michaeli
,
et al.
UInvariant Sampling: Extrapolation and Causal Interpolation From Gene...
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Citations
(491)
Convex multiclass segmentation with shearlet regularization
S. Häuser
,
G. Steidl
Journal:
International Journal of Computer Mathematics  IJCM
, vol. aheadofp, no. aheadofp, pp. 120, 2012
Fusion Frames and the Restricted Isometry Property
Bernhard G. Bodmann
,
Jameson Cahill
,
Peter G. Casazza
Journal:
Numerical Functional Analysis and Optimization  NUMER FUNC ANAL OPTIMIZ
, vol. 33, no. 79, pp. 770790, 2012
Sufficient conditions and stability of wavelet superframes
Zhijing Zhao
,
Wenchang Sun
Journal:
Applicable Analysis
, vol. 91, no. 7, pp. 13931406, 2012
Sparse fusion frames: existence and construction
(
Citations: 4
)
Robert Calderbank
,
Peter G. Casazza
,
Andreas Heinecke
,
Gitta Kutyniok
,
Ali Pezeshki
Journal:
Advances in Computational Mathematics  Adv. Comput. Math.
, vol. 35, no. 1, pp. 131, 2011
UInvariant Sampling: Extrapolation and Causal Interpolation From Generalized Samples
(
Citations: 3
)
Tomer Michaeli
,
Volker Pohl
,
Yonina C. Eldar
Journal:
IEEE Transactions on Signal Processing  TSP
, vol. 59, no. 5, pp. 20852100, 2011