scholarly journals Characterization of Oblique Dual Frame Pairs

2006 ◽  
Vol 2006 (1) ◽  
Author(s):  
Yonina C. Eldar ◽  
Ole Christensen
Keyword(s):  
Dual Frame ◽  
Dual Frame Pairs ◽  
Oblique Dual

Dilation of Dual Frame Pairs in Hilbert C*-Modules

2011 ◽  
Vol 63 (1-2) ◽  
pp. 241-250 ◽  
Author(s):  
Deguang Han ◽  
Wu Jing ◽  
David Larson ◽  
Pengtong Li ◽  
Ram N. Mohapatra
Keyword(s):  
Dual Frame ◽  
Dual Frame Pairs

Extension of Bessel sequences to oblique dual frame sequences and the minimal projection

2015 ◽  
Vol 30 ◽  
Author(s):  
Yoo Koo ◽  
Jae Lim
Keyword(s):  
Dual Frame ◽  
Minimal Projection ◽  
Generating Sets ◽  
Shift Invariant Spaces ◽  
Oblique Dual ◽  
Bessel Sequences ◽  
Invariant Spaces

An extension of two Bessel sequences to oblique dual frame sequences and its applications to shift-invariant spaces are considered. The best-known situation where this kind of extension is necessary is the construction of a pair of biorthogonal multiresolution analyses, where two generating sets whose shifts are only assumed to be Bessel sequences are given. This extension naturally leads to consideration of the ‘minimal projection’ extending two closed subspaces. The existence or non-existence of the minimal projection is discussed.

scholarly journals A note on finite dual frame pairs

2012 ◽  
Vol 140 (11) ◽  
pp. 3921-3930 ◽  
Author(s):  
Ole Christensen ◽  
Alexander M. Powell ◽  
Xiang Chun Xiao
Keyword(s):  
Dual Frame ◽  
Dual Frame Pairs

OBLIQUE DUAL FRAMES IN FINITE-DIMENSIONAL HILBERT SPACES

2013 ◽  
Vol 11 (02) ◽  
pp. 1350011 ◽  
Author(s):  
XIANG-CHUN XIAO ◽  
YU-CAN ZHU ◽  
XIAO-MING ZENG
Keyword(s):  
Hilbert Spaces ◽  
Computational Efficiency ◽  
Tight Frame ◽  
Constructive Method ◽  
Dual Frame ◽  
Dual Frames ◽  
Finite Dimensional ◽  
Oblique Dual

A frame can be completed to a tight frame by adding some additional vectors. However, for the purpose of computational efficiency, we need to put restrictions to the number of added vectors. In this paper we propose a constructive method that allows to extend a given frame to an oblique dual frame pair such that the number of added vectors is in general much smaller than the number of added vectors used to extend it to a tight frame. We also present a uniqueness characterization and several equivalent characterizations for an oblique dual frame pair, it turns out that oblique dual frame pair provides more flexibilities than alternate dual frame pair.

DISCRETE-TIME WILSON FRAMES WITH GENERAL LATTICES

2012 ◽  
Vol 10 (05) ◽  
pp. 1250044 ◽  
Author(s):  
QIAOFANG LIAN ◽  
YUNFANG LIAN ◽  
MINGHOU YOU
Keyword(s):  
Discrete Time ◽  
Tight Frame ◽  
Gabor Frame ◽  
Dual Frame ◽  
Necessary And Sufficient Condition ◽  
Dual Frames ◽  
Gabor Dual ◽  
Bessel Sequences ◽  
Necessary And Sufficient

In this paper, we focus on the construction of Wilson frames and their dual frames for general lattices of volume [Formula: see text] (K even) in the discrete-time setting. We obtain a necessary and sufficient condition for two Bessel sequences having Wilson structure to be dual frames for l2(ℤ). When the window function satisfies some symmetry property, we obtain a characterization of a Wilson system to be a tight frame for l2(ℤ), show that a Wilson frame for l2(ℤ) can be derived from the underlying Gabor frame, and that the dual frame having Wilson structure can also be derived from the canonical Gabor dual of the underlying Gabor frame.

Wilson frames for ℂL with general lattices

2016 ◽  
Vol 14 (06) ◽  
pp. 1650055
Author(s):  
Minghou You ◽  
Junqiao Yang ◽  
Qiaofang Lian
Keyword(s):  
Digital Signal ◽  
Tight Frame ◽  
Gabor Frame ◽  
Dual Frame ◽  
Dual Frames ◽  
Volume Formula ◽  
Discrete Signals ◽  
Gabor Dual ◽  
Necessary And Sufficient

In digital signal and image processing one can only process discrete signals of finite length, and the space [Formula: see text] is the preferred setting. Recently, Kutyniok and Strohmer constructed orthonormal Wilson bases for [Formula: see text] with general lattices of volume [Formula: see text] ([Formula: see text] even). In this paper, we extend this construction to Wilson frames for [Formula: see text] with general lattices of volume [Formula: see text], where [Formula: see text] and [Formula: see text]. We obtain a necessary and sufficient condition for two sequences having Wilson structure to be dual frames for [Formula: see text]. When the window function satisfies some symmetry property, we obtain a characterization of a Wilson system to be a tight frame for [Formula: see text], show that a Wilson frame for [Formula: see text] can be derived from the underlying Gabor frame, and that the dual frame having Wilson structure can also be derived from the canonical Gabor dual of the underlying Gabor frame.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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