<?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>0123-2126</journal-id>
<journal-title><![CDATA[Ingeniería y Universidad]]></journal-title>
<abbrev-journal-title><![CDATA[Ing. Univ.]]></abbrev-journal-title>
<issn>0123-2126</issn>
<publisher>
<publisher-name><![CDATA[Pontificia Universidad Javeriana]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0123-21262017000200213</article-id>
<article-id pub-id-type="doi">10.11144/javeriana.iyu21-2.rsic</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Recovering Spectral Images from Compressive Measurements using Designed Coded Apertures and Matrix Completion Theory]]></article-title>
<article-title xml:lang="es"><![CDATA[Reconstrucción de imágenes espectrales desde medidas compresas usando aperturas codificadas diseñadas y la teoría de estimación de elementos de matrices incompletas]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gelvez]]></surname>
<given-names><![CDATA[Tatiana]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rueda]]></surname>
<given-names><![CDATA[Hoover]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Arguello]]></surname>
<given-names><![CDATA[Henry]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af3">
<institution><![CDATA[,Universidad Industrial de Santander  ]]></institution>
<addr-line><![CDATA[Bucaramanga ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,niversidad de Delaware  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>USA</country>
</aff>
<aff id="Af5">
<institution><![CDATA[,Universidad Industrial de Santander  ]]></institution>
<addr-line><![CDATA[Bucaramanga ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<volume>21</volume>
<numero>2</numero>
<fpage>213</fpage>
<lpage>229</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0123-21262017000200213&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0123-21262017000200213&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0123-21262017000200213&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Introducción: Compressive spectral imaging (CSI) captures spectral information at various spatial locations of a spectral image with few compressed projections. Traditionally, the original scene is recovered by assuming sparsity in some known representation basis. In contrast, the matrix completion techniques (MC) rely on a low-rank structure that avoids using any known representation basis. The coded aperture snapshot spectral imager (CASSI) is a CSI optical architecture that modulates light by using a coded aperture with a pattern that determines the quality of reconstruction. The objective of this paper is to design optimal coded aperture patterns when MC is used to recover a spectral scene from CASSI measurements. Metodología: The patterns are attained by maximizing the distance between the translucent elements, which become more precise measurements given the MC constraints. Resultados: Simulations from different databases show an average improvement of 1 to 9 dBs when the designed patterns are used compared to the conventional random and complementary patterns. Discusión y conclusiones: The proposed approach solves an integer optimization problem with a complexity that is commonly NP-hard but that can be reduced with proper relaxation. Finally, an effective alternative method using coded aperture patterns for MC to solve the inverse compressive spectral imaging problem is presented. for MC to solve the inverse compressive spectral imaging problem is presented.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Introducción: La adquisición compresiva de imágenes espectrales (CSI) captura información espectral en varios puntos espaciales de una escena con pocas proyecciones comprimidas. La escena original es tradicionalmente recuperada asumiendo baja densidad en alguna base de representación conocida. En contraste, la teoría de estimación de elementos de matrices incompletas (MC) asume una estructura de bajo rango que evita conocer una base de representación. El sistema óptico de adquisición de imágenes espectrales de única captura (CASSI) modula la luz usando una apertura codificada cuyo patrón determina la calidad de la reconstrucción. Por ello, este trabajo propone diseñar patrones óptimos para usar MC en la recuperación de una escena a partir de medidas comprimidas. Metodología: Los patrones diseñados maximizan la distancia entre los elementos translúcidos para generar medidas más adecuadas según las restricciones de MC. Resultados: Simulaciones con diferentes escenas muestran una mejora promedio entre 1-9 dBs cuando los patrones diseñados son usados comparado con los patrones aleatorios y complementarios tradicionales. Discusión y conclusiones: El enfoque propuesto implica resolver un problema de optimización con enteros cuya complejidad es NP-complejo, pero que puede ser relajada y reducida. Finalmente, se propuso una alternativa efectiva para resolver el problema inverso de imágenes espectrales usando patrones diseñados y la técnica MC.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[matrix completion]]></kwd>
<kwd lng="en"><![CDATA[spectral imaging]]></kwd>
<kwd lng="en"><![CDATA[optimization problems]]></kwd>
<kwd lng="en"><![CDATA[compressive sensing]]></kwd>
<kwd lng="en"><![CDATA[coded apertures]]></kwd>
<kwd lng="es"><![CDATA[teoría de estimación de elementos de matrices incompletas]]></kwd>
<kwd lng="es"><![CDATA[imágenes espectrales]]></kwd>
<kwd lng="es"><![CDATA[problema de optimización]]></kwd>
<kwd lng="es"><![CDATA[muestreo comprimido]]></kwd>
<kwd lng="es"><![CDATA[aperturas codificadas]]></kwd>
</kwd-group>
</article-meta>
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