<?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>0120-6230</journal-id>
<journal-title><![CDATA[Revista Facultad de Ingeniería Universidad de Antioquia]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.fac.ing.univ. Antioquia]]></abbrev-journal-title>
<issn>0120-6230</issn>
<publisher>
<publisher-name><![CDATA[Facultad de Ingeniería, Universidad de Antioquia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-62302017000200072</article-id>
<article-id pub-id-type="doi">10.17533/udea.redin.n83a10</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[An algorithm for learning sparsifying transforms of multidimensional signals]]></article-title>
<article-title xml:lang="es"><![CDATA[Algoritmo de aprendizaje de diccionarios para transformación de imágenes multidimensionales en señales dispersas]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hurtado-Camacho]]></surname>
<given-names><![CDATA[Óscar Enrique]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rueda-Chacon]]></surname>
<given-names><![CDATA[Hoover Fabián]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Arguello-Fuentes]]></surname>
<given-names><![CDATA[Henry]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Industrial de Santander Escuela de Ingeniería de Sistemas e Informática ]]></institution>
<addr-line><![CDATA[Bucaramanga ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,University of Delaware Department of Electrical and Computer Engineering ]]></institution>
<addr-line><![CDATA[Newark DE]]></addr-line>
<country>USA</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2017</year>
</pub-date>
<numero>83</numero>
<fpage>72</fpage>
<lpage>81</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-62302017000200072&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-62302017000200072&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-62302017000200072&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT Multidimensional signals contain information of an object in more than one dimension, and usually their processing relies on complex methods in comparison with their unidimensional counterparts. In signal processing, finding a sparse representation of a signal is of great importance for compression purposes. Analytical multidimensional bases such as the Fourier, Cosine, or Wavelet Transform have been conventionally used. Recently, the use of learned dictionaries that directly adapt to the given signal are becoming popular in tasks such as image classification, image denoising, spectral unmixing, and medical image reconstruction. This paper presents an algorithm to learn transformation bases for the sparse representation of multidimensional signals. The proposed algorithm alternates between a sparse coding step solved by hard or soft thresholding strategies, and an updating dictionary step solved by a conjugate gradient method. Furthermore, the algorithm is tested using both: two-dimensional and three-dimensional patches, which are compared in terms of the sparsity performance for different types of multidimensional signals such as hyperspectral images, computerized axial tomography images and, magnetic resonance images. The attained results are compared against traditional analytical transforms and the state-of-the-art dictionary learning method: K-SVD.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Las señales multidimensionales contienen información de un objeto en más de una dimensión y, comúnmente, su procesamiento requiere métodos de mayor complejidad que las señales unidimensionales. En procesamiento de señales, la representación escasa de una señal es de gran importancia para fines de compresión. Convencionalmente, transformaciones analíticas como las transformadas de Fourier, Coseno o Wavelet, han sido utilizadas. Recientemente, se ha popularizado el uso de diccionarios entrenados, que se adaptan a una señal dada, en aplicaciones como clasificación de imágenes, eliminación de ruido, separación espectral, y reconstrucción de imágenes médicas. Este artículo presenta un algoritmo para entrenar bases de transformación para representación escasa de señales multidimensionales. El algoritmo propuesto alterna entre una codificación escasa que se resuelve por umbralización, y la actualización del diccionario que se resuelve mediante el método de gradiente conjugado. Además, el artículo incluye una comparación entre parches bidimensionales y tridimensionales en términos del nivel de escasez que ofrecen en diferentes tipos de señales multidimensionales como: imágenes hiperespectrales, imágenes de tomografía computarizada, e imágenes de resonancia magnética. Los resultados obtenidos son comparados contra transformaciones analíticas tradicionales y contra el método de entrenamiento de diccionarios más conocido en el estado del arte: K-SVD.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[sparse representation]]></kwd>
<kwd lng="en"><![CDATA[dictionary learning]]></kwd>
<kwd lng="en"><![CDATA[sparsifying transforms]]></kwd>
<kwd lng="en"><![CDATA[multidimensional signal processing]]></kwd>
<kwd lng="es"><![CDATA[representación escasa]]></kwd>
<kwd lng="es"><![CDATA[aprendizaje de diccionarios]]></kwd>
<kwd lng="es"><![CDATA[transformadas para escasez]]></kwd>
<kwd lng="es"><![CDATA[procesamiento de imágenes multidimensionales]]></kwd>
</kwd-group>
</article-meta>
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