Perturbation of Regular Sampling in Shift-Invariant Spaces for Frames

2006 ◽  
Vol 52 (10) ◽  
pp. 4643-4648 ◽  
Author(s):  
P. Zhao ◽  
C. Zhao ◽  
P.G. Casazza
Keyword(s):  
Regular Sampling ◽  
Shift Invariant Spaces ◽  
Invariant Spaces

scholarly journals Regular and Irregular Sampling Theorem for Multiwavelet Subspaces

2010 ◽  
Vol 2010 ◽  
pp. 1-18
Author(s):  
Liu Zhanwei ◽  
Hu Guoen ◽  
Wu Guochang
Keyword(s):  
Sampling Theorem ◽  
Irregular Sampling ◽  
Sufficient Condition ◽  
Regular Sampling ◽  
Shift Invariant Spaces ◽  
Invariant Spaces

We study the sampling theorem for frames in multiwavelet subspaces. Firstly, a sufficient condition under which the regular sampling theorem holds is established. Then, notice that irregular sampling is also useful in practice; we consider the general cases of the irregular sampling and establish a general irregular sampling theorem for multiwavelet subspaces. Finally, using this generalized irregular sampling theorem, we obtain an estimate for the perturbations of regular sampling in shift-invariant spaces.

GENERALIZED IRREGULAR SAMPLING IN SHIFT-INVARIANT SPACES

2007 ◽  
Vol 05 (03) ◽  
pp. 369-387 ◽  
Author(s):  
ANTONIO G. GARCÍA ◽  
GERARDO PÉREZ-VILLALÓN
Keyword(s):  
Sampling Period ◽  
Sampling Theory ◽  
Irregular Sampling ◽  
Natural Consequence ◽  
Invariant Space ◽  
Starting Point ◽  
Regular Sampling ◽  
Shift Invariant Spaces ◽  
Invariant Spaces ◽  
Shift Invariant Space

This article concerns the problem of stable recovering of any function in a shift-invariant space from irregular samples of some filtered versions of the function itself. These samples arise as a perturbation of regular samples. The starting point is the generalized regular sampling theory which allows any function f in a shift-invariant space to be recovered from the samples at {rn}n∈ℤ of s filtered versions [Formula: see text] of f, where the number of channels s is greater or equal than the sampling period r. These regular samples can be expressed as the frame coefficients of a function related to f in L2(0,1) with respect to certain frame for L2(0,1). The irregular samples are also obtained as a perturbation of the aforesaid frame. As a natural consequence, the irregular sampling results arise from the theory of perturbation of frames. The paper concludes by putting the theory to work in some spline examples where Kadec-type results are obtained.

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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