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
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Latest Advances in Fundamental Theories of Signal Processing)
Category: INVITED
Keyword: 
sampling theorem,  inverse problem,  image restoration,  computerized tomography,  supervised learning, 

Full Text: PDF(384.9KB)

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.