Error estimation for non-uniform sampling in shift invariant space

Abstract

To reconstruct a function from its sampling value is not always exact, error may arise due to a lot of reasons, therefore error estimation is useful in reconstruction. For non-uniform sampling in shift invariant space, three kinds of errors of the reconstruction formula are discussed in this article. For every kind of error, we give an estimation. We find the accuracy of the reconstruction formula mainly depends on the decay property of the generator and the sampling function.

Keywords:

• Shift invariant space
• Nonuniform sampling
• Error estimation
• Riesz basis
• Frame
• Reproducing kernel

Keywords:

• AMS (2000): 42C15
• 41A15
• 46A35
• 46N99
• 47B37
• 94A12

Acknowledgement

I would like to thank the editors for their warm-hearted help.