What Can We See behind Sampling Theorems?

Hidemitsu OGAWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.3   pp.688-695
Publication Date: 2009/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.688
Print ISSN: 0916-8508
Type of Manuscript: INVITED PAPER (Special Section on Latest Advances in Fundamental Theories of Signal Processing)
Category: 
Keyword: 
sampling theorem,  inverse problem,  image restoration,  computerized tomography,  supervised learning,  

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Summary: 
This paper shows that there is a fruitful world behind sampling theorems. For this purpose, the sampling problem is reformulated from a functional analytic standpoint, and is consequently revealed that the sampling problem is a kind of inverse problem. The sampling problem covers, for example, signal and image restoration including super resolution, image reconstruction from projections such as CT scanners in hospitals, and supervised learning such as learning in artificial neural networks. An optimal reconstruction operator is also given, providing the best approximation to an individual original signal without our knowing the original signal.