Construction of highly redundant incoherent unit norm tight frames as a union of orthonormal bases

2019 ◽  
Vol 54 ◽  
pp. 101401
Author(s):  
Pradip Sasmal ◽  
Phanindra Jampana ◽  
C.S. Sastry
Keyword(s):  
Tight Frames ◽  
Orthonormal Bases ◽  
Unit Norm

scholarly journals Tetris Tight Frames Construction via Hadamard Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
A. Abdollahi ◽  
M. Monfaredpour
Keyword(s):  
Hadamard Matrices ◽  
New Method ◽  
Tight Frames ◽  
Frame Operator ◽  
Elementary Construction ◽  
Unit Norm

We present a new method to construct unit norm tight frames by applying altered Hadamard matrices. Also we determine an elementary construction which can be used to produce a unit norm frame with prescribed spectrum of frame operator.

scholarly journals KACZMARZ ALGORITHM AND FRAMES

2013 ◽  
Vol 11 (05) ◽  
pp. 1350036 ◽  
Author(s):  
WOJCIECH CZAJA ◽  
JAMES H. TANIS
Keyword(s):  
Infinite System ◽  
Frame Theory ◽  
Riesz Bases ◽  
Tight Frames ◽  
Algebraic Equations ◽  
Orthonormal Bases ◽  
Kaczmarz Algorithm ◽  
Linear Algebraic Equations ◽  
Bounded Matrices ◽  
Unit Vectors

Sequences of unit vectors for which the Kaczmarz algorithm always converges in Hilbert space can be characterized in frame theory by tight frames with constant 1. We generalize this result to the context of frames and bases. In particular, we show that the only effective sequences which are Riesz bases are orthonormal bases. Moreover, we consider the infinite system of linear algebraic equations Ax = b and characterize the (bounded) matrices A for which the Kaczmarz algorithm always converges to a solution.

Connectivity of spaces of finite unit-norm tight frames

2015 ◽  
Author(s):  
Jameson Cahill ◽  
Dustin Mixon ◽  
Nate Strawn
Keyword(s):  
Tight Frames ◽  
Unit Norm

scholarly journals Connectivity and Irreducibility of Algebraic Varieties of Finite Unit Norm Tight Frames

2017 ◽  
Vol 1 (1) ◽  
pp. 38-72 ◽  
Author(s):  
Jameson Cahill ◽  
Dustin G. Mixon ◽  
Nate Strawn
Keyword(s):  
Tight Frames ◽  
Algebraic Varieties ◽  
Unit Norm

scholarly journals Gabor systems on positive half line via Walsh-Fourier transform

2020 ◽  
Vol 12 (2) ◽  
pp. 468-482
Author(s):  
O. Ahmad ◽  
N.A. Sheikh
Keyword(s):  
Fourier Transform ◽  
Applied Mathematics ◽  
Vital Role ◽  
Complete Characterization ◽  
Half Line ◽  
Tight Frames ◽  
Gabor Systems ◽  
Orthonormal Bases ◽  
Positive Half

Gabor systems play a vital role not only in modern harmonic analysis but also in several fields of applied mathematics, for instances, detection of chirps, or image processing. In this paper, we investigate Gabor systems on positive half line via Walsh-Fourier transform. We provide the complete characterization of orthogonal Gabor systems on positive half line. Furthermore, we provide the characterization of tight frames and orthonormal bases of Gabor systems on positive half line in Fourier domain.

scholarly journals Modulated Unit-Norm Tight Frames for Compressed Sensing

2015 ◽  
Vol 63 (15) ◽  
pp. 3974-3985 ◽  
Author(s):  
Peng Zhang ◽  
Lu Gan ◽  
Sumei Sun ◽  
Cong Ling
Keyword(s):  
Compressed Sensing ◽  
Tight Frames ◽  
Unit Norm

scholarly journals Moving finite unit norm tight frames for $S^{n}$

2014 ◽  
Vol 58 (2) ◽  
pp. 311-322 ◽  
Author(s):  
Daniel Freeman ◽  
Ryan Hotovy ◽  
Eileen Martin
Keyword(s):  
Tight Frames ◽  
Unit Norm

Construction of Incoherent Unit Norm Tight Frames With Application to Compressed Sensing

2014 ◽  
Vol 60 (4) ◽  
pp. 2319-2330 ◽  
Author(s):  
Evaggelia V. Tsiligianni ◽  
Lisimachos P. Kondi ◽  
Aggelos K. Katsaggelos
Keyword(s):  
Compressed Sensing ◽  
Tight Frames ◽  
Unit Norm
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