<?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>1405-5546</journal-id>
<journal-title><![CDATA[Computación y Sistemas]]></journal-title>
<abbrev-journal-title><![CDATA[Comp. y Sist.]]></abbrev-journal-title>
<issn>1405-5546</issn>
<publisher>
<publisher-name><![CDATA[Instituto Politécnico Nacional, Centro de Investigación en Computación]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-55462020000200469</article-id>
<article-id pub-id-type="doi">10.13053/cys-24-2-3372</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Fast Convergence of the Two Dimensional Discrete Shearlet Transform]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Navarro Fuentes]]></surname>
<given-names><![CDATA[Jaime]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Herrera Alcántara]]></surname>
<given-names><![CDATA[Oscar]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma Metropolitana Departamento de Ciencias Básicas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma Metropolitana Departamento de Sistemas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2020</year>
</pub-date>
<volume>24</volume>
<numero>2</numero>
<fpage>469</fpage>
<lpage>480</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-55462020000200469&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-55462020000200469&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-55462020000200469&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: The 2D discrete shearlet transform for a given function  f in    L 2  (   &#8477; 2 ) has been defined through dilation, shear and translation parameters in such a way that the continuity of  f at    (  0 , 0 ) can be studied by means of the convergence of the discrete shearlet transform as the dilation parameter converges to zero. Computer experiments illustrate this property by detecting edges in images that correspond to discontinuities.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Shearlets]]></kwd>
<kwd lng="en"><![CDATA[tight frames]]></kwd>
<kwd lng="en"><![CDATA[continuity]]></kwd>
<kwd lng="en"><![CDATA[image processing]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Easley]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Labate]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Lim]]></surname>
<given-names><![CDATA[W.Q.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sparse directional image representations using the discrete shearlet transform]]></article-title>
<source><![CDATA[Appl. Comput. Harmon. Anal.]]></source>
<year>2008</year>
<volume>25</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>25-46</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Labate]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Lim]]></surname>
<given-names><![CDATA[W.Q.]]></given-names>
</name>
<name>
<surname><![CDATA[Kutyniok]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Weiss]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Sparse multidimensional representation using shearlets]]></source>
<year>2005</year>
<volume>5914</volume>
<conf-name><![CDATA[ SPIE Wavelets XI]]></conf-name>
<conf-loc> </conf-loc>
<page-range>254-62</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Guo]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Kutyniok]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Labate]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sparse multidimensional representations using anisotropic dilation and shear operators]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Lai]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Wavelets and Splines]]></source>
<year>2006</year>
<publisher-loc><![CDATA[Brentwood ]]></publisher-loc>
<publisher-name><![CDATA[Nashboro Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Navarro]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Wavelet transforms and singularities of L2-functions in Rn]]></article-title>
<source><![CDATA[Revista Colombiana de Matemáticas]]></source>
<year>1998</year>
<volume>32</volume>
<page-range>93-9</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Navarro]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Herrera]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Convergence of the discrete wavelet transform]]></article-title>
<source><![CDATA[Int. J. Wavelets Multi.]]></source>
<year>2012</year>
<volume>10</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1-12</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Daubechies]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ten lectures on wavelets]]></source>
<year>1992</year>
<publisher-loc><![CDATA[Philadelphia ]]></publisher-loc>
<publisher-name><![CDATA[SIAM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Navarro]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Herrera]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Decay properties of the discrete wavelet transform in n dimensions with independent dilation parameters]]></article-title>
<source><![CDATA[J. Inequal. Appl.]]></source>
<year>2016</year>
<page-range>1-19</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kugarajah]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Qinghua]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Multidimensional wavelet frames]]></article-title>
<source><![CDATA[IEEE Trans. Neural Netw.]]></source>
<year>1995</year>
<volume>6</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1552-6</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dahlke]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Kutyniok]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Maass]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Sagiv]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Stark]]></surname>
<given-names><![CDATA[H.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Teschke]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The uncertainty principle associated with the continuous shearlet transform]]></article-title>
<source><![CDATA[Int. J. Wavelets Multi.]]></source>
<year>2008</year>
<volume>6</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>157-81</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kutyniok]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Labate]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Resolution of the wavefront set using continuous shearlets]]></article-title>
<source><![CDATA[Trans. Amer. Math. Soc.]]></source>
<year>2009</year>
<volume>36</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>2719-54</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Goossens]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Aelterman]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Luong]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Pizurica]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Philips]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<source><![CDATA[Efficient design of a low redundant discrete shearlet transform]]></source>
<year>2009</year>
<conf-name><![CDATA[ LNLA:2009 Int. Workshop on Local and Non-Local approximation in Image Proccesing]]></conf-name>
<conf-loc> </conf-loc>
<page-range>112-24</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kutyniok]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Lim]]></surname>
<given-names><![CDATA[W.Q.]]></given-names>
</name>
<name>
<surname><![CDATA[Reisenhofer]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[ShearLab 3D: Faithful digital shearlet transforms based on compactly supported shearlets]]></article-title>
<source><![CDATA[ACM Trans. Math. Software]]></source>
<year>2016</year>
<volume>42</volume>
<numero>5</numero>
<issue>5</issue>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
