scholarly journals A phaseless reconstruction algorithm for real-valued signals in a shift-invariant space

2018 ◽  
Vol 48 (10) ◽  
pp. 1237
Author(s):  
Chen Yang ◽  
Cheng Cheng ◽  
Sun Qiyu
Keyword(s):  
Reconstruction Algorithm ◽  
Invariant Space ◽  
Shift Invariant Space

Reconstruction of compressed samples in shift-invariant space base on matrix factorization

2011 ◽  
Vol 37 (3) ◽  
pp. 311-318
Author(s):  
Zhaoxuan Zhu ◽  
Houjun Wang ◽  
Zhigang Wang ◽  
Hao Zhang
Keyword(s):  
Matrix Factorization ◽  
Invariant Space ◽  
Shift Invariant Space

REFINABLE SHIFT INVARIANT SPACES IN ℝd

2005 ◽  
Vol 03 (03) ◽  
pp. 321-345
Author(s):  
CARLOS A. CABRELLI ◽  
SIGRID B. HEINEKEN ◽  
URSULA M. MOLTER
Keyword(s):  
Dimensional Subspace ◽  
Finite Dimensional Subspace ◽  
Invariant Space ◽  
Refinement Equation ◽  
Compactly Supported Function ◽  
Dilation Matrix ◽  
Jordan Basis ◽  
Shift Invariant Spaces ◽  
Invariant Spaces ◽  
Shift Invariant Space

Let φ : ℝd → ℂ be a compactly supported function which satisfies a refinement equation of the form [Formula: see text] where Γ ⊂ ℝd is a lattice, Λ is a finite subset of Γ, and A is a dilation matrix. We prove, under the hypothesis of linear independence of the Γ-translates of φ, that there exists a correspondence between the vectors of the Jordan basis of a finite submatrix of L = [cAi-j]i,j∈Γ and a finite-dimensional subspace [Formula: see text] in the shift-invariant space generated by φ. We provide a basis of [Formula: see text] and show that its elements satisfy a property of homogeneity associated to the eigenvalues of L. If the function φ has accuracy κ, this basis can be chosen to contain a basis for all the multivariate polynomials of degree less than κ. These latter functions are associated to eigenvalues that are powers of the eigenvalues of A-1. Furthermore we show that the dimension of [Formula: see text] coincides with the local dimension of φ, and hence, every function in the shift-invariant space generated by φ can be written locally as a linear combination of translates of the homogeneous functions.

scholarly journals Invariance of a Shift-Invariant Space in Several Variables

2010 ◽  
Vol 5 (4) ◽  
pp. 1031-1050 ◽  
Author(s):  
Magalí Anastasio ◽  
Carlos Cabrelli ◽  
Victoria Paternostro
Keyword(s):  
Invariant Space ◽  
Several Variables ◽  
Shift Invariant Space

scholarly journals Invariance of a Shift-Invariant Space

2009 ◽  
Vol 16 (1) ◽  
pp. 60-75 ◽  
Author(s):  
Akram Aldroubi ◽  
Carlos Cabrelli ◽  
Christopher Heil ◽  
Keri Kornelson ◽  
Ursula Molter
Keyword(s):  
Invariant Space ◽  
Shift Invariant Space

MULTI-CHANNEL SAMPLING ON SHIFT-INVARIANT SPACES WITH FRAME GENERATORS

2012 ◽  
Vol 10 (01) ◽  
pp. 1250003 ◽  
Author(s):  
A. G. GARCIA ◽  
J. M. KIM ◽  
K. H. KWON ◽  
G. J. YOON
Keyword(s):  
Continuous Function ◽  
Sufficient Conditions ◽  
Sampling Theory ◽  
Invariant Space ◽  
Frame Sequence ◽  
Shift Invariant Spaces ◽  
Necessary And Sufficient ◽  
Invariant Spaces ◽  
Sampling Expansions ◽  
Shift Invariant Space

Let φ be a continuous function in L2(ℝ) such that the sequence {φ(t - n)}n∈ℤ is a frame sequence in L2(ℝ) and assume that the shift-invariant space V(φ) generated by φ has a multi-banded spectrum σ(V). The main aim in this paper is to derive a multi-channel sampling theory for the shift-invariant space V(φ). By using a type of Fourier duality between the spaces V(φ) and L2[0, 2π] we find necessary and sufficient conditions allowing us to obtain stable multi-channel sampling expansions in V(φ).

Sign in / Sign up

Export Citation Format

Share Document