DOI:

https://doi.org/10.14483/23448393.17240

Publicado:

2021-05-30

Número:

Vol. 26 Núm. 2 (2021): Mayo-Agosto

Sección:

Ingeniería de Sistemas

Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal

Blurred Image Restoration Using a Regularized Linear Programming Model

Autores/as

Palabras clave:

Image restoration, Inverse Problems, Linear programming, L1 norm based regularization (en).

Palabras clave:

Restauraci´on de im´agenes, problemas inversos, programaci´on lineal, regularizaci´on en norma L1 (es).

Resumen (es)

Contexto: Los problemas de minimizaci´on en el sentido de los mínimos cuadrados han sido constantemente usados en la restauraci´on de im´agenes borrosas. Estos se caracterizan por ser sensibles a valores at´ıpicos afectando significativamente la calidad de la imagen restaurada. Teniendo en cuenta que la norma-L1 es menos sensible a datos at´ıpicos, el problema de restauraci´on de im´agenes borrosas se plantea como un problema de programaci´on lineal.

M´etodo: Un m´etodo de punto interior se utiliza para la soluci´on del problema de programaci´on lineal. Se presenta la adaptaci´on de t´ecnicas de regularización de la imagen buscada y su derivada, al problema de programaci´on lineal. Se realiza un estudio comparativo con otras t´ecnicas de restauraci´on bajo diferentes tipos de difuminado de im´agenes.

Resultados: Se prob´o que el m´etodo propuesto conduce a mejoras notables en la im´agenes recuperadas.
Los experimentos num´ericos muestran que el m´etodo de programaci´on lineal funciona mucho mejor
que los propuestos en la literatura, en t´erminos de valores de PSNR, SSIM y en la calidad visual de las
im´agenes reconstruidas.

Conclusiones: El problema de programaci´on lineal regularizado puede utilizarse eficazmente como
modelo matem´atico del problema de restauraci´on de im´agenes borrosas. Para trabajos futuros se plantea
el estudio de la selecci´on autom´atica de par´ametros de regularizaci´on y soluci´on de restauraci´on sin
conocimiento previo del n´ucleo de difuminado.

Resumen (en)

Context: Minimization problems in the sense of least squares have constantly been used in the restoration
of blurred images. These are characterized by their sensitivity to outliers affecting the quality of
the restored image significantly. Since the L1-norm is less sensitive to outliers, the image deblurring
problem is posed as a linear programming problem.
Method: An interior point method is used to solve the linear programming problem. The adaptation of
regularization techniques, of the image sought and its derivative, to the problem of linear programming
is presented. A comparative study with other restoration methods under different types of image blurring
is carried out.
Results: The proposed method leads to remarkable improvements in the recovered images. Numerical
experiments show that the linear programming method works much better than those proposed in the
literature, in terms of PSNR, SSIM values and in the visual quality of the reconstructed images.
Conclusions: The regularized linear programming problem can be effectively used as a mathematical
model of the image deblurring problem. For future work, it is planned to study of the automatic selection
of regularization parameters and restoration solutions without prior knowledge of blur kernel.
Keywords: Image restoration, Inverse Problems, Linear programming, L1 norm based regularization.

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Cómo citar

APA

Ruiz Vera, J. M., & Exequiel Fuentes, J. (2021). Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal. Ingeniería, 26(2). https://doi.org/10.14483/23448393.17240

ACM

[1]
Ruiz Vera, J.M. y Exequiel Fuentes, J. 2021. Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal. Ingeniería. 26, 2 (may 2021). DOI:https://doi.org/10.14483/23448393.17240.

ACS

(1)
Ruiz Vera, J. M.; Exequiel Fuentes, J. Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal. Ing. 2021, 26.

ABNT

RUIZ VERA, J. M.; EXEQUIEL FUENTES, J. Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal. Ingeniería, [S. l.], v. 26, n. 2, 2021. DOI: 10.14483/23448393.17240. Disponível em: https://revistas.udistrital.edu.co/index.php/reving/article/view/17240. Acesso em: 15 jun. 2021.

Chicago

Ruiz Vera, Jorge Mauricio, y José Exequiel Fuentes. 2021. «Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal». Ingeniería 26 (2). https://doi.org/10.14483/23448393.17240.

Harvard

Ruiz Vera, J. M. y Exequiel Fuentes, J. (2021) «Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal», Ingeniería, 26(2). doi: 10.14483/23448393.17240.

IEEE

[1]
J. M. Ruiz Vera y J. Exequiel Fuentes, «Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal», Ing., vol. 26, n.º 2, may 2021.

MLA

Ruiz Vera, J. M., y J. Exequiel Fuentes. «Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal». Ingeniería, vol. 26, n.º 2, mayo de 2021, doi:10.14483/23448393.17240.

Turabian

Ruiz Vera, Jorge Mauricio, y José Exequiel Fuentes. «Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal». Ingeniería 26, no. 2 (mayo 30, 2021). Accedido junio 15, 2021. https://revistas.udistrital.edu.co/index.php/reving/article/view/17240.

Vancouver

1.
Ruiz Vera JM, Exequiel Fuentes J. Restauraci´on de im´agenes borrosas usando un modelo regularizado de programaci´on lineal. Ing. [Internet]. 30 de mayo de 2021 [citado 15 de junio de 2021];26(2). Disponible en: https://revistas.udistrital.edu.co/index.php/reving/article/view/17240

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