Noise filtering and deconvolution of XPS data by wavelets and Fourier transform
In experimental sciences, the recorded data are often modelled as the noisy convolution product of an instrumental response with the ‘true’ signal to find. Different models have been used for interpreting x‐ray photoelectron spectroscopy (XPS) spectra. This article suggests a method of estimate the...
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| Veröffentlicht in: | Surface and interface analysis 2004-01, Vol.36 (1), p.71-80 |
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| container_title | Surface and interface analysis |
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| creator | Charles, Catherine Leclerc, Gervais Louette, Pierre Rasson, Jean-Paul Pireaux, Jean-Jacques |
| description | In experimental sciences, the recorded data are often modelled as the noisy convolution product of an instrumental response with the ‘true’ signal to find. Different models have been used for interpreting x‐ray photoelectron spectroscopy (XPS) spectra. This article suggests a method of estimate the ‘true’ XPS signal that relies upon the use of wavelets, which, because they exhibit simultaneous time and frequency localization, are well suited to signal analysis.
First, a wavelet shrinkage algorithm is used to filter the noise. This is achieved by decomposing the noisy signal into an appropriate wavelet basis and then thresholding the wavelet coefficients that contain noise. This algorithm has a particular threshold related to frequency and time.
Secondly, the broadening due to the instrumental response is eliminated through a deconvolution process similar to that developed in the previous paper in this series for the analysis of HREELS data. This step mainly rests on least‐squares and on the existing relation between the Fourier transform, the wavelet transform and the convolution product. Copyright © 2004 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/sia.1650 |
| format | Article |
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First, a wavelet shrinkage algorithm is used to filter the noise. This is achieved by decomposing the noisy signal into an appropriate wavelet basis and then thresholding the wavelet coefficients that contain noise. This algorithm has a particular threshold related to frequency and time.
Secondly, the broadening due to the instrumental response is eliminated through a deconvolution process similar to that developed in the previous paper in this series for the analysis of HREELS data. This step mainly rests on least‐squares and on the existing relation between the Fourier transform, the wavelet transform and the convolution product. Copyright © 2004 John Wiley & Sons, Ltd.</description><identifier>ISSN: 0142-2421</identifier><identifier>EISSN: 1096-9918</identifier><identifier>DOI: 10.1002/sia.1650</identifier><identifier>CODEN: SIANDQ</identifier><language>eng</language><publisher>Chichester, UK: John Wiley & Sons, Ltd</publisher><subject>Condensed matter: electronic structure, electrical, magnetic, and optical properties ; Condensed matter: structure, mechanical and thermal properties ; Cross-disciplinary physics: materials science; rheology ; deconvolution ; Exact sciences and technology ; Physics ; Poisson noise ; wavelets ; XPS</subject><ispartof>Surface and interface analysis, 2004-01, Vol.36 (1), p.71-80</ispartof><rights>Copyright © 2004 John Wiley & Sons, Ltd.</rights><rights>2005 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3620-d580d3bfbc1fb5dbb4d05e7fef1780e89052b66f4a4d509a8d23bc3306472c993</citedby><cites>FETCH-LOGICAL-c3620-d580d3bfbc1fb5dbb4d05e7fef1780e89052b66f4a4d509a8d23bc3306472c993</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fsia.1650$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fsia.1650$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,4024,27923,27924,27925,45574,45575</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15862483$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Charles, Catherine</creatorcontrib><creatorcontrib>Leclerc, Gervais</creatorcontrib><creatorcontrib>Louette, Pierre</creatorcontrib><creatorcontrib>Rasson, Jean-Paul</creatorcontrib><creatorcontrib>Pireaux, Jean-Jacques</creatorcontrib><title>Noise filtering and deconvolution of XPS data by wavelets and Fourier transform</title><title>Surface and interface analysis</title><addtitle>Surf. Interface Anal</addtitle><description>In experimental sciences, the recorded data are often modelled as the noisy convolution product of an instrumental response with the ‘true’ signal to find. Different models have been used for interpreting x‐ray photoelectron spectroscopy (XPS) spectra. This article suggests a method of estimate the ‘true’ XPS signal that relies upon the use of wavelets, which, because they exhibit simultaneous time and frequency localization, are well suited to signal analysis.
First, a wavelet shrinkage algorithm is used to filter the noise. This is achieved by decomposing the noisy signal into an appropriate wavelet basis and then thresholding the wavelet coefficients that contain noise. This algorithm has a particular threshold related to frequency and time.
Secondly, the broadening due to the instrumental response is eliminated through a deconvolution process similar to that developed in the previous paper in this series for the analysis of HREELS data. This step mainly rests on least‐squares and on the existing relation between the Fourier transform, the wavelet transform and the convolution product. Copyright © 2004 John Wiley & Sons, Ltd.</description><subject>Condensed matter: electronic structure, electrical, magnetic, and optical properties</subject><subject>Condensed matter: structure, mechanical and thermal properties</subject><subject>Cross-disciplinary physics: materials science; rheology</subject><subject>deconvolution</subject><subject>Exact sciences and technology</subject><subject>Physics</subject><subject>Poisson noise</subject><subject>wavelets</subject><subject>XPS</subject><issn>0142-2421</issn><issn>1096-9918</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><recordid>eNp10EtLAzEUhuEgCtYL-BOyUdyMniQzmcxSxFZBqqCidBMyuUh0OtFk2tp_79QWXbk6m4cXzofQEYEzAkDPk1dnhBewhQYEKp5VFRHbaAAkpxnNKdlFeym9AYBggg_Q3Tj4ZLHzTWejb1-xag02Vod2HppZ50OLg8Mv9w_YqE7heokXam4b26UfOQyz6G3EXVRtciFOD9COU02yh5u7j56GV4-X19nt3ejm8uI204xTyEwhwLDa1Zq4ujB1nRsobOmsI6UAKyooaM25y1VuCqiUMJTVmjHgeUl1VbF9dLLufsTwObOpk1OftG0a1dowS5IKWpUlET08XUMdQ0rROvkR_VTFpSQgV4vJfjG5Wqynx5umSlo1rv9J-_TnC8FpLljvsrVb-MYu_-3Jh5uLTXfjfers169X8V3ykpWFfB6PJH0c5ZNyMpacfQNeZYi4</recordid><startdate>200401</startdate><enddate>200401</enddate><creator>Charles, Catherine</creator><creator>Leclerc, Gervais</creator><creator>Louette, Pierre</creator><creator>Rasson, Jean-Paul</creator><creator>Pireaux, Jean-Jacques</creator><general>John Wiley & Sons, Ltd</general><general>Wiley</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>8BQ</scope><scope>8FD</scope><scope>JG9</scope></search><sort><creationdate>200401</creationdate><title>Noise filtering and deconvolution of XPS data by wavelets and Fourier transform</title><author>Charles, Catherine ; Leclerc, Gervais ; Louette, Pierre ; Rasson, Jean-Paul ; Pireaux, Jean-Jacques</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3620-d580d3bfbc1fb5dbb4d05e7fef1780e89052b66f4a4d509a8d23bc3306472c993</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Condensed matter: electronic structure, electrical, magnetic, and optical properties</topic><topic>Condensed matter: structure, mechanical and thermal properties</topic><topic>Cross-disciplinary physics: materials science; rheology</topic><topic>deconvolution</topic><topic>Exact sciences and technology</topic><topic>Physics</topic><topic>Poisson noise</topic><topic>wavelets</topic><topic>XPS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Charles, Catherine</creatorcontrib><creatorcontrib>Leclerc, Gervais</creatorcontrib><creatorcontrib>Louette, Pierre</creatorcontrib><creatorcontrib>Rasson, Jean-Paul</creatorcontrib><creatorcontrib>Pireaux, Jean-Jacques</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><jtitle>Surface and interface analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Charles, Catherine</au><au>Leclerc, Gervais</au><au>Louette, Pierre</au><au>Rasson, Jean-Paul</au><au>Pireaux, Jean-Jacques</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Noise filtering and deconvolution of XPS data by wavelets and Fourier transform</atitle><jtitle>Surface and interface analysis</jtitle><addtitle>Surf. Interface Anal</addtitle><date>2004-01</date><risdate>2004</risdate><volume>36</volume><issue>1</issue><spage>71</spage><epage>80</epage><pages>71-80</pages><issn>0142-2421</issn><eissn>1096-9918</eissn><coden>SIANDQ</coden><abstract>In experimental sciences, the recorded data are often modelled as the noisy convolution product of an instrumental response with the ‘true’ signal to find. Different models have been used for interpreting x‐ray photoelectron spectroscopy (XPS) spectra. This article suggests a method of estimate the ‘true’ XPS signal that relies upon the use of wavelets, which, because they exhibit simultaneous time and frequency localization, are well suited to signal analysis.
First, a wavelet shrinkage algorithm is used to filter the noise. This is achieved by decomposing the noisy signal into an appropriate wavelet basis and then thresholding the wavelet coefficients that contain noise. This algorithm has a particular threshold related to frequency and time.
Secondly, the broadening due to the instrumental response is eliminated through a deconvolution process similar to that developed in the previous paper in this series for the analysis of HREELS data. This step mainly rests on least‐squares and on the existing relation between the Fourier transform, the wavelet transform and the convolution product. Copyright © 2004 John Wiley & Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/sia.1650</doi><tpages>10</tpages></addata></record> |
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| subjects | Condensed matter: electronic structure, electrical, magnetic, and optical properties Condensed matter: structure, mechanical and thermal properties Cross-disciplinary physics: materials science rheology deconvolution Exact sciences and technology Physics Poisson noise wavelets XPS |
| title | Noise filtering and deconvolution of XPS data by wavelets and Fourier transform |
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