On norms of operators generated by shift transformations arising in signal and image processing on meshes supplied with semigroup structures

11th International Conference on "Mesh methods for boundary-value problems and applications"

Gumerov, R.N.^1

Department of Mathematical Analysis, N.I. Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kremlevskaya 35, Kazan, Tatarstan

420008, Russia^1

关键词: Linear operators;    Polynomial filters;    Real-world;    Semi-group;    Shift operators;    Signal and image processing;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012042/pdf
DOI  :  10.1088/1757-899X/158/1/012042

来源: IOP

【 摘 要 】

Shift transformations and linear operators generated by shifts have a number of applications in signal and image processing. This note is concerned with a problem which has arisen in studying properties of real-world signals and images defined on meshes. For processing we suggest to introduce in domains of signals and images different semigroup structures. Semigroup operations give us opportunities to introduce shift transformations of signals and images. We study norms of polynomial filters generated by shift operators.