Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms

Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms

This work presents an algorithm to reduce the multiplicative computational complexity in the creation of digital holograms, where an object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image. The image is modeled usin...

Full description

Bibliographic Details
Main Authors: Agustín Pérez-Ramírez, Julian Guerrero Juk, Rafael Sanchez-Lara, Joel Antonio Trejo-Sánchez, Lelio de la Cruz-May
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2017/5612743
id doaj-aa9da5b999f34b7e96fb929129cf9ff0
record_format Article
spelling doaj-aa9da5b999f34b7e96fb929129cf9ff02020-11-25T00:35:47ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472017-01-01201710.1155/2017/56127435612743Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital HologramsAgustín Pérez-Ramírez0Julian Guerrero Juk1Rafael Sanchez-Lara2Joel Antonio Trejo-Sánchez3Lelio de la Cruz-May4Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Autopista del Sol Km 104, Real del Puente, 62790 Xochitepec, MOR, MexicoTecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Autopista del Sol Km 104, Real del Puente, 62790 Xochitepec, MOR, MexicoFacultad de Ingeniería, Universidad Autónoma del Carmen, 24180 Ciudad del Carmen, CAM, MexicoCONACyT-Centro de Investigación en Matemáticas, 97205 Mérida, YUC, MexicoFacultad de Ingeniería, Universidad Autónoma del Carmen, 24180 Ciudad del Carmen, CAM, MexicoThis work presents an algorithm to reduce the multiplicative computational complexity in the creation of digital holograms, where an object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image. The image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity (k-1)N2 for the case of sparse matrices or binary images, where k is the number of pixels other than zero and N2 is the total of points in the image.http://dx.doi.org/10.1155/2017/5612743
collection DOAJ
language English
format Article
sources DOAJ
author Agustín Pérez-Ramírez
Julian Guerrero Juk
Rafael Sanchez-Lara
Joel Antonio Trejo-Sánchez
Lelio de la Cruz-May
spellingShingle Agustín Pérez-Ramírez
Julian Guerrero Juk
Rafael Sanchez-Lara
Joel Antonio Trejo-Sánchez
Lelio de la Cruz-May
Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms
Mathematical Problems in Engineering
author_facet Agustín Pérez-Ramírez
Julian Guerrero Juk
Rafael Sanchez-Lara
Joel Antonio Trejo-Sánchez
Lelio de la Cruz-May
author_sort Agustín Pérez-Ramírez
title Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms
title_short Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms
title_full Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms
title_fullStr Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms
title_full_unstemmed Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms
title_sort application of mathematical symmetrical group theory in the creation process of digital holograms
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2017-01-01
description This work presents an algorithm to reduce the multiplicative computational complexity in the creation of digital holograms, where an object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image. The image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity (k-1)N2 for the case of sparse matrices or binary images, where k is the number of pixels other than zero and N2 is the total of points in the image.
url http://dx.doi.org/10.1155/2017/5612743
work_keys_str_mv AT agustinperezramirez applicationofmathematicalsymmetricalgrouptheoryinthecreationprocessofdigitalholograms
AT julianguerrerojuk applicationofmathematicalsymmetricalgrouptheoryinthecreationprocessofdigitalholograms
AT rafaelsanchezlara applicationofmathematicalsymmetricalgrouptheoryinthecreationprocessofdigitalholograms
AT joelantoniotrejosanchez applicationofmathematicalsymmetricalgrouptheoryinthecreationprocessofdigitalholograms
AT leliodelacruzmay applicationofmathematicalsymmetricalgrouptheoryinthecreationprocessofdigitalholograms
_version_ 1725307704297127936

Similar Items