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We select the Luminous Infrared Galaxies by cross-correlating the FaintSource Catalogue (FSC) and Point Source Catalogue (PSC) of the IRAS Survey withthe Second Data Release of the SDSS for studying their infrared and opticalproperties. The total number of our sample is 1267 for FSC and 427 for PSC byusing 2$\sigma$ significance level cross-section. The "likelihood ratio" methodis used to estimate the sample's reliability and for a more reliable subsample(908 for FSC and 356 for PSC) selection. Then a Catalog with both the infrared,optical and radio informations is presented and will be used in further works.Some statistical results show that the Luminous Infrared Galaxies are quitedifferent from the Ultra-Luminous Infrared Galaxies. The AGN fractions ofgalaxies with different infrared luminosities and the radio to infraredcorrelations are consist with previous studies.Comment: 15 pages, 11 figures. Accepted by ChJAA. Reference adde

A Catalog of Luminous Infrared Galaxies in the IRAS Survey and Second Data Release of SDSS