Paper Info
Title
The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties
Abstract
The uncertainty principle is a fundamental concept in the context of signal and image processing, just as much as it has been in the framework of physics and more recently in harmonic analysis. Uncertainty principles can be derived by using a group theoretic approach. This approach yields also a formalism for finding functions which are the minimizers of the uncertainty principles. A general theorem which associates an uncertainty principle with a pair of self-adjoint operators is used in finding the minimizers of the uncertainty related to various groups.This study is concerned with the uncertainty principle in the context of the Weyl-Heisenberg, the SIM(2), the Affine and the Affine-Weyl-Heisenberg groups. We explore the relationship between the two-dimensional affine group and the SIM (2) group in terms of the uncertainty minimizers. The uncertainty principle is also extended to the Affine-Weyl-Heisenberg group in one dimension. Possible minimizers related to these groups are also presented and the scale-space properties of some of the minimizers are explored.
Year
DOI
Venue
2006
10.1007/s10851-006-8301-4
Journal of Mathematical Imaging and Vision
Keywords
Field
DocType
uncertainty principles,minimal uncertainty states,affine weyl-heisenberg group,scale-space properties
Affine transformation,Applied mathematics,Mathematical optimization,Entropic uncertainty,Uncertainty principle,Mathematical analysis,Conjugate variables,Scale space,Harmonic analysis,Operator (computer programming),Affine group,Mathematics
Journal
Volume
Issue
ISSN
26
1-2
0924-9907
Citations 
PageRank 
References 
4
1.17
16
Authors
3
Name
Order
Citations
PageRank
Chen Sagiv116210.74
Nir A. Sochen267263.76
Yehoshua Y. Zeevi3610248.69