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Restauración de imágenes borrosas usando programación lineal
dc.rights.license | Atribución-NoComercial-SinDerivadas 4.0 Internacional |
dc.contributor.advisor | Ruiz Vera, Jorge Mauricio |
dc.contributor.author | Fuentes Gil, José Exequiel |
dc.date.accessioned | 2020-09-22T18:50:17Z |
dc.date.available | 2020-09-22T18:50:17Z |
dc.date.issued | 2020-09-04 |
dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/78488 |
dc.description.abstract | In the process of capturing images, it is common to deal with deteriorated images. These appear in various fields such as: astronomy, medicine, among others. In this work, a method is developed for the restoration of blurred images based on the approach of poorly proposed integral equations. The solution of the integral equation is seen as the minimum of a limited optimization problem in the norm $ || \cdot ||_{L_1}$. In this way, it is expressed as a linear programming problem. Also, it was found that the problem needs to be adapted to the particular image restoration problem by adding additional terms to the originally proposed model. In addition, evaluating its efficiency and effectiveness, this method is shown to be competitive with respect to other ones, and it can be used in different environments, showing satisfactory results. |
dc.description.abstract | En el proceso de captura de imágenes es común tratar con imágenes deterioradas. Estas aparecen en diversos ámbitos como lo son: astronomía, medicina, entre otros. En este trabajo se desarrolla un método para la restauración de imágenes borrosas basado en el planteamiento de ecuaciones integrales mal propuestas. La solución de la ecuación integral es vista como el mínimo de un problema de optimización considerado en la norma $||\cdot||_{L_1}$. De esta forma es expresado como un problema de programación lineal. También, se encontró que el problema debe ser adaptado al caso particular de la restauración de imágenes agregando términos extra al modelo originalmente propuesto. Además de evaluar su eficiencia y eficacia, se muestra que este método es competitivo con respecto a otros propuestos inicialmente y que puede ser usado en diferentes ámbitos mostrando resultados satisfactorios. |
dc.format.extent | 104 |
dc.format.mimetype | application/pdf |
dc.language.iso | spa |
dc.rights | Derechos reservados - Universidad Nacional de Colombia |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.subject.ddc | 510 - Matemáticas |
dc.subject.ddc | 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas |
dc.subject.ddc | 510 - Matemáticas::518 - Análisis numérico |
dc.title | Restauración de imágenes borrosas usando programación lineal |
dc.type | Otro |
dc.rights.spa | Acceso abierto |
dc.description.additional | Línea de Investigación: Matemática aplicada, procesamiento de imágenes |
dc.type.driver | info:eu-repo/semantics/other |
dc.type.version | info:eu-repo/semantics/acceptedVersion |
dc.publisher.program | Bogotá - Ciencias - Maestría en Ciencias - Matemática Aplicada |
dc.description.degreelevel | Maestría |
dc.publisher.department | Departamento de Matemáticas |
dc.publisher.branch | Universidad Nacional de Colombia - Sede Bogotá |
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dc.rights.accessrights | info:eu-repo/semantics/openAccess |
dc.subject.proposal | Imágenes borrosas |
dc.subject.proposal | Blurry images |
dc.subject.proposal | Problemas inversos |
dc.subject.proposal | Ill posed problems |
dc.subject.proposal | Problemas mal propuestos |
dc.subject.proposal | Inverse problems |
dc.subject.proposal | Linear programming |
dc.subject.proposal | Programación lineal |
dc.subject.proposal | Regularización |
dc.subject.proposal | Regularization |
dc.type.coar | http://purl.org/coar/resource_type/c_1843 |
dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa |
dc.type.content | Text |
oaire.accessrights | http://purl.org/coar/access_right/c_abf2 |
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