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- Title
Sampling Theorem with Optimum Noise Suppression.
- Authors
Ogawa, Hidemitsu; Hirabayashi, Akira
- Abstract
We propose sampling theorems that reconstruct the optimal approximation under a certain criterion from a finite number of degraded, noisy, sampled values. In that criterion, we minimize the average difference between a reconstructed function and an individual target function over a noise ensemble subject to the condition that the reconstructed function is an unbiased estimator of the best approximation obtainable from noiseless sampled values. We devise a general form for sampling theorems with a real pulse and with an ideal pulse, thus providing the optimal estimator even for a singular noise covariance matrix. The relationship between the proposed criterion and the Gauss-Markov estimator is also discussed. Finally, we clarify the relationship between the best approximation and the interpolation.
- Subjects
STATISTICAL sampling; RANDOM noise theory; MODULES (Algebra); GAUSSIAN Markov random fields; APPROXIMATION theory; INTERPOLATION
- Publication
Sampling Theory in Signal & Image Processing, 2007, Vol 6, Issue 2, p167
- ISSN
1530-6429
- Publication type
Article
- DOI
10.1007/bf03549470