<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0121-750X</journal-id>
<journal-title><![CDATA[Ingeniería]]></journal-title>
<abbrev-journal-title><![CDATA[ing.]]></abbrev-journal-title>
<issn>0121-750X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Distrital Francisco José de Caldas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-750X2021000200254</article-id>
<article-id pub-id-type="doi">10.14483/23448393.17240</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Restauración de imágenes borrosas usando un modelo regularizado de programación lineal]]></article-title>
<article-title xml:lang="en"><![CDATA[Blurred Image Restoration Using a Regularized Linear Programming Model]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Fuentes]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ruiz V]]></surname>
<given-names><![CDATA[Jorge Mauricio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Bogotà ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional de Colombia Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Bogotà ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>08</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>08</month>
<year>2021</year>
</pub-date>
<volume>26</volume>
<numero>2</numero>
<fpage>254</fpage>
<lpage>272</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-750X2021000200254&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-750X2021000200254&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-750X2021000200254&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  Contexto:  Los problemas de minimización en el sentido de los mínimos cuadrados han sido constantemente usados en la restauración de imágenes borrosas. Estos se caracterizan por ser sensibles a valores atípicos afectando significativamente la calidad de la imagen restaurada. Teniendo en cuenta que la norma L1 es menos sensible a datos atípicos, el problema de restauración de imágenes borrosas se plantea como un problema de programación lineal.  Método:  Un método de punto interior se utiliza para la solución del problema de programación lineal. Se presenta la adaptación de técnicas de regularización al problema de programación lineal de la imagen buscada y su derivada. Se realiza un estudio comparativo con otras técnicas de restauración bajo diferentes tipos de difuminado de imágenes.  Resultados:  Se probó que el método propuesto conduce a mejoras notables en las imágenes recuperadas. Los experimentos numéricos muestran que el método de programación lineal funciona mucho mejor que los propuestos en la literatura, en términos de valores de PSNR, SSIM y en la calidad visual de las imágenes reconstruidas.  Conclusiones:  El problema de programación lineal regularizado puede utilizarse eficazmente como modelo matemático del problema de restauración de imágenes borrosas. Para trabajos futuros se plantea el estudio de la selección automática de parámetros de regularización y solución de restauración sin conocimiento previo del núcleo de difuminado.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  Context:  Minimization problems in the sense of least squares have constantly been used in the restoration of blurred images. They are characterized by their sensitivity to outliers, which significantly affects affecting the quality of the restored image relevantly. 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. This article presents the adaptation of regularization techniques of the image sought and its derivative to the problem of linear programming. A comparative study with other restoration methods under different types of image blurring is conducted.  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 and SSIM values, as well as 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, there are plans to study of the automatic selection of regularization parameters and restoration solutions without prior knowledge of the blur kernel.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[restauración de imágenes]]></kwd>
<kwd lng="es"><![CDATA[problemas inversos]]></kwd>
<kwd lng="es"><![CDATA[programación lineal]]></kwd>
<kwd lng="es"><![CDATA[regularización en norma L1.]]></kwd>
<kwd lng="en"><![CDATA[Image restoration]]></kwd>
<kwd lng="en"><![CDATA[inverse problems]]></kwd>
<kwd lng="en"><![CDATA[linear programming]]></kwd>
<kwd lng="en"><![CDATA[L1 norm based regularization.]]></kwd>
</kwd-group>
</article-meta>
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