Reconstruction from convolution random sampling in local shift invariant spaces

2019 ◽  
Vol 35 (12) ◽  
pp. 125008 ◽  
Author(s):  
Yaxu Li ◽  
Jinming Wen ◽  
Jun Xian
Keyword(s):  
Random Sampling ◽  
Shift Invariant Spaces ◽  
Local Shift ◽  
Invariant Spaces

Random sampling and reconstruction in multiply generated shift-invariant spaces

2019 ◽  
Vol 17 (02) ◽  
pp. 323-347 ◽  
Author(s):  
Jianbin Yang
Keyword(s):  
Random Sampling ◽  
Stability Problem ◽  
Approximate Formula ◽  
Reconstruction Algorithm ◽  
Finite Dimensional ◽  
Shift Invariant Spaces ◽  
The Stability ◽  
Sampling And Reconstruction ◽  
Invariant Spaces ◽  
Sampling Set

Shift-invariant spaces play an important role in approximation theory, wavelet analysis, finite elements, etc. In this paper, we consider the stability and reconstruction algorithm of random sampling in multiply generated shift-invariant spaces [Formula: see text]. Under some decay conditions of the generator [Formula: see text], we approximate [Formula: see text] with finite-dimensional subspaces and prove that with overwhelming probability, the stability of sampling set conditions holds uniformly for all functions in certain compact subsets of [Formula: see text] when the sampling size is sufficiently large. Moreover, we show that this stability problem is connected with properties of the random matrix generated by [Formula: see text]. In the end, we give a reconstruction algorithm for the random sampling of functions in [Formula: see text].

scholarly journals Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Maria Charina ◽  
Vladimir Yu. Protasov
Keyword(s):  
Analytic Functions ◽  
Finitely Generated ◽  
Subdivision Schemes ◽  
Exponential Polynomials ◽  
Compactly Supported ◽  
Shift Invariant Spaces ◽  
Local Shift ◽  
Invariant Spaces

AbstractIn this paper we characterize all subspaces of analytic functions in finitely generated shift-invariant spaces with compactly supported generators and provide explicit descriptions of their elements. We illustrate the differences between our characterizations and Strang-Fix or zero conditions on several examples. Consequently, we depict the analytic functions generated by scalar or vector subdivision with masks of bounded and unbounded support. In particular, we prove that exponential polynomials are indeed the only analytic limits of level dependent scalar subdivision schemes with finitely supported masks.

scholarly journals Shift-invariant spaces from rotation-covariant functions

2008 ◽  
Vol 25 (2) ◽  
pp. 240-265 ◽  
Author(s):  
Brigitte Forster ◽  
Thierry Blu ◽  
Dimitri Van De Ville ◽  
Michael Unser
Keyword(s):  
Shift Invariant Spaces ◽  
Invariant Spaces
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