• 淮卿
    了解作者
  • matlab
    开发工具
  • 7.5MB
    文件大小
  • rar
    文件格式
  • 0
    收藏次数
  • 10 积分
    下载积分
  • 3
    下载次数
  • 2020-06-09 10:40
    上传日期
小波去噪的ViruShrink和BayesShrink算法实现,含源代码及LaTeX报告
小波去噪.rar
  • 小波去噪
  • Report
  • main1.synctex.gz
    74.4KB
  • boat.eps
    339KB
  • main1.pdf
    4.4MB
  • hyderabad-eps-converted-to.pdf
    247.3KB
  • sjtu-badge-eps-converted-to.pdf
    29.7KB
  • hyderabad.eps
    328.2KB
  • draft.bib
    331B
  • main1.tex.bak
    30.5KB
  • main1.tex
    30.4KB
  • lena.png
    147.7KB
  • sjtu-badge.eps
    279.1KB
  • main1.aux
    3.4KB
  • IEEEtran.cls
    197.9KB
  • hyderabad512.png
    219.8KB
  • main1.blg
    673B
  • lena.eps
    338.3KB
  • main1.log
    57.3KB
  • main1.bbl
    901B
  • cording
  • udaymain.asv
    7.2KB
  • bayes.m
    253B
  • wavework.p
    6.8KB
  • friendgray.jpg
    116.3KB
  • raodecompduplicate.asv
    6.4KB
  • mainuday
    6.5KB
  • sthresh.m
    277B
  • wpsnr.asv
    2.8KB
  • friend.jpg
    468.7KB
  • boat.png
    173.6KB
  • lena.png
    147.7KB
  • Thumbs.db
    42.5KB
  • wpsnr.m
    2.8KB
  • raomain.m
    6.8KB
  • wavefilter.p
    6.6KB
  • hyderabad512.png
    219.8KB
  • bayes.pdf
    424.7KB
  • chapter4.doc
    11KB
  • wavecopy.p
    779B
  • cameraman.jpg
    41.5KB
  • compare11.m
    669B
  • wavefast.p
    7.2KB
  • wave2gray.p
    7.7KB
  • wavecut.p
    814B
内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/626918e30990925c0441c859/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626918e30990925c0441c859/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Image<span class="_ _0"> </span>Denoising<span class="_ _0"> </span>Based<span class="_ _0"> </span>on<span class="_ _0"> </span>Adapti<span class="_ _1"></span>v<span class="_ _1"></span>e<span class="_ _0"> </span>W<span class="_ _2"></span>a<span class="_ _1"></span>velet</div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">Thresholding</div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc0 ls0 ws0">Abstract<span class="ff3">&#8212;In<span class="_ _3"> </span>this<span class="_ _3"> </span>paper<span class="_ _4"></span>,<span class="_ _3"> </span>we<span class="_ _3"> </span>introduce<span class="_ _5"> </span>the<span class="_ _5"> </span>wavelet<span class="_ _5"> </span>based</span></div><div class="t m0 x4 h4 y4 ff3 fs1 fc0 sc0 ls0 ws0">image<span class="_ _6"> </span>denoising<span class="_ _6"> </span>algorithms<span class="_ _6"> </span>and<span class="_ _6"> </span>discuss<span class="_ _6"> </span>two<span class="_ _6"> </span>kinds<span class="_ _6"> </span>of<span class="_ _6"> </span>wa<span class="_ _7"></span>velet</div><div class="t m0 x4 h4 y5 ff3 fs1 fc0 sc0 ls0 ws0">shrinking<span class="_ _8"> </span>methods(wav<span class="_ _7"></span>elet<span class="_ _8"> </span>soft-threholding):V<span class="_ _1"></span>iruShrink<span class="_ _8"> </span>[1]<span class="_ _8"> </span>and</div><div class="t m0 x4 h4 y6 ff3 fs1 fc0 sc0 ls0 ws0">BayesShrink<span class="_ _5"> </span>[2].<span class="_ _5"> </span>W<span class="_ _4"></span>e<span class="_ _5"> </span>introduce<span class="_ _5"> </span>these<span class="_ _5"> </span>two<span class="_ _9"> </span>methods<span class="_ _9"> </span>in<span class="_ _5"> </span>detail</div><div class="t m0 x4 h4 y7 ff3 fs1 fc0 sc0 ls0 ws0">and<span class="_ _3"> </span>implement<span class="_ _a"> </span>extensive<span class="_ _5"> </span>experiments<span class="_ _a"> </span>on<span class="_ _3"> </span>different<span class="_ _3"> </span>kinds<span class="_ _a"> </span>of</div><div class="t m0 x4 h4 y8 ff3 fs1 fc0 sc0 ls0 ws0">grey<span class="_ _8"> </span>images<span class="_ _b"> </span>with<span class="_ _8"> </span>different<span class="_ _b"> </span>wav<span class="_ _7"></span>elet<span class="_ _8"> </span>functions.<span class="_ _b"> </span>The<span class="_ _b"> </span>experimental</div><div class="t m0 x4 h4 y9 ff3 fs1 fc0 sc0 ls0 ws0">results<span class="_ _c"> </span>pro<span class="_ _7"></span>ve<span class="_ _c"> </span>the<span class="_ _d"> </span>effectiveness<span class="_ _c"> </span>of<span class="_ _c"> </span>wavelet<span class="_ _c"> </span>shrinking<span class="_ _c"> </span>based<span class="_ _d"> </span>method.</div><div class="t m0 x4 h4 ya ff3 fs1 fc0 sc0 ls0 ws0">V<span class="_ _7"></span>iruShrink<span class="_ _8"> </span>is<span class="_ _b"> </span>more<span class="_ _8"> </span>rob<span class="_ _7"></span>ust<span class="_ _8"> </span>but<span class="_ _8"> </span>BayesShrink<span class="_ _8"> </span>performs<span class="_ _8"> </span>better<span class="_ _b"> </span>in</div><div class="t m0 x4 h4 yb ff3 fs1 fc0 sc0 ls0 ws0">most<span class="_ _e"> </span>cases</div><div class="t m0 x3 h3 yc ff2 fs1 fc0 sc0 ls0 ws0">Keyw<span class="_ _1"></span>ords<span class="ff3">&#8212;</span>Image<span class="_ _a"> </span>denoising,<span class="_ _a"> </span>wavelet<span class="_ _3"> </span>thresholding,<span class="_ _a"> </span>adaptive</div><div class="t m0 x4 h3 yd ff2 fs1 fc0 sc0 ls0 ws0">method</div><div class="t m0 x5 h5 ye ff1 fs2 fc0 sc0 ls0 ws0">I<span class="_ _f"></span>.<span class="_ _10"> </span>I<span class="_ _f"></span><span class="fs3">N<span class="_ _f"></span>T<span class="_ _f"></span>RO<span class="_ _f"></span>D<span class="_ _f"></span>U<span class="_ _f"></span>C<span class="_ _f"></span>T<span class="_ _f"></span>I<span class="_ _f"></span>O<span class="_ _f"></span>N</span></div><div class="t m0 x4 h6 yf ff3 fs4 fc0 sc0 ls0 ws0">N</div><div class="t m0 x6 h5 y10 ff1 fs2 fc0 sc0 ls0 ws0">O<span class="_ _f"></span>I<span class="_ _f"></span>S<span class="_ _f"></span>E<span class="_ _11"> </span>produced<span class="_ _b"> </span>in<span class="_ _b"> </span>image<span class="_ _11"> </span>acquisition<span class="_ _b"> </span>and<span class="_ _b"> </span>transformation</div><div class="t m0 x7 h5 yf ff1 fs2 fc0 sc0 ls0 ws0">would<span class="_"> </span>cause<span class="_"> </span>image<span class="_"> </span>quality<span class="_ _d"> </span>decline,<span class="_ _d"> </span>so<span class="_"> </span>image<span class="_ _d"> </span>denoising<span class="_ _d"> </span>is</div><div class="t m0 x4 h5 y11 ff1 fs2 fc0 sc0 ls0 ws0">one<span class="_ _e"> </span>of<span class="_ _8"> </span>the<span class="_ _e"> </span>most<span class="_ _e"> </span>fundamental<span class="_ _8"> </span>and<span class="_ _e"> </span>important<span class="_ _8"> </span>image<span class="_ _e"> </span>processing</div><div class="t m0 x4 h5 y12 ff1 fs2 fc0 sc0 ls0 ws0">techniques.<span class="_ _d"> </span>The<span class="_ _12"> </span>goal<span class="_ _d"> </span>of<span class="_ _12"> </span>denoising<span class="_ _d"> </span>is<span class="_ _12"> </span>to<span class="_ _d"> </span>remove<span class="_"> </span>the<span class="_ _12"> </span>noise<span class="_ _d"> </span>while</div><div class="t m0 x4 h5 y13 ff1 fs2 fc0 sc0 ls0 ws0">retaining<span class="_ _d"> </span>as<span class="_ _12"> </span>much<span class="_ _12"> </span>as<span class="_ _d"> </span>possible<span class="_ _12"> </span>the<span class="_ _d"> </span>important<span class="_ _12"> </span>signal<span class="_ _12"> </span>features.<span class="_ _d"> </span>As</div><div class="t m0 x4 h5 y14 ff1 fs2 fc0 sc0 ls0 ws0">in<span class="_"> </span>many<span class="_"> </span>occasions<span class="_ _c"> </span>image<span class="_"> </span>noise<span class="_"> </span>can<span class="_"> </span>be<span class="_ _c"> </span>approximated<span class="_"> </span>with<span class="_"> </span>addi-</div><div class="t m0 x4 h5 y15 ff1 fs2 fc0 sc0 ls0 ws0">tiv<span class="_ _1"></span>e<span class="_ _e"> </span>Gaussian<span class="_ _12"> </span>white<span class="_ _12"> </span>noise,<span class="_ _12"> </span>the<span class="_ _12"> </span>key<span class="_ _12"> </span>point<span class="_ _12"> </span>of<span class="_ _12"> </span>image<span class="_ _e"> </span>denoising<span class="_ _12"> </span>is</div><div class="t m0 x4 h5 y16 ff1 fs2 fc0 sc0 ls0 ws0">how<span class="_ _c"> </span>to<span class="_"> </span>remo<span class="_ _7"></span>ve<span class="_"> </span>this<span class="_"> </span>kind<span class="_ _c"> </span>of<span class="_"> </span>noise.<span class="_"> </span>T<span class="_ _1"></span>raditionally<span class="_ _4"></span>,<span class="_"> </span>this<span class="_"> </span>is<span class="_"> </span>achiev<span class="_ _7"></span>ed</div><div class="t m0 x4 h5 y17 ff1 fs2 fc0 sc0 ls0 ws0">by<span class="_ _e"> </span>linear<span class="_ _e"> </span>processing<span class="_ _e"> </span>such<span class="_ _e"> </span>as<span class="_ _8"> </span>W<span class="_ _1"></span>iener<span class="_ _e"> </span>&#64257;ltering.<span class="_ _8"> </span>Ho<span class="_ _7"></span>wev<span class="_ _1"></span>er,<span class="_ _e"> </span>man<span class="_ _7"></span>y</div><div class="t m0 x4 h5 y18 ff1 fs2 fc0 sc0 ls0 ws0">nonlinear<span class="_ _11"> </span>methods<span class="_ _11"> </span>based<span class="_ _13"> </span>on<span class="_ _11"> </span>wav<span class="_ _7"></span>elet<span class="_ _11"> </span>transforms<span class="_ _11"> </span>can<span class="_ _13"> </span>achiev<span class="_ _1"></span>e</div><div class="t m0 x4 h5 y19 ff1 fs2 fc0 sc0 ls0 ws0">better<span class="_ _e"> </span>performance.</div><div class="t m0 x8 h5 y1a ff1 fs2 fc0 sc0 ls0 ws0">The<span class="_ _d"> </span>basic<span class="_ _12"> </span>principle<span class="_ _12"> </span>of<span class="_ _d"> </span>image<span class="_ _12"> </span>denoising<span class="_ _12"> </span>is<span class="_ _d"> </span>to<span class="_ _12"> </span>&#64257;lter<span class="_ _12"> </span>the<span class="_ _d"> </span>noise</div><div class="t m0 x4 h5 y1b ff1 fs2 fc0 sc0 ls0 ws0">by<span class="_ _e"> </span>some<span class="_ _12"> </span>kind<span class="_ _e"> </span>of<span class="_ _e"> </span>&#64257;lter<span class="_ _1"></span>,<span class="_ _e"> </span>and<span class="_ _e"> </span>keep<span class="_ _12"> </span>the<span class="_ _e"> </span>original<span class="_ _e"> </span>image<span class="_ _e"> </span>content<span class="_ _12"> </span>as</div><div class="t m0 x4 h5 y1c ff1 fs2 fc0 sc0 ls0 ws0">intact<span class="_ _12"> </span>as<span class="_ _12"> </span>possible.<span class="_ _12"> </span>The<span class="_ _e"> </span>multi-resolution<span class="_ _12"> </span>representation<span class="_ _12"> </span>capabil-</div><div class="t m0 x4 h5 y1d ff1 fs2 fc0 sc0 ls0 ws0">ity<span class="_ _11"> </span>of<span class="_ _13"> </span>wav<span class="_ _7"></span>elet<span class="_ _11"> </span>transform<span class="_ _13"> </span>has<span class="_ _13"> </span>been<span class="_ _11"> </span>proven<span class="_ _11"> </span>to<span class="_ _13"> </span>be<span class="_ _13"> </span>very<span class="_ _11"> </span>useful</div><div class="t m0 x4 h5 y1e ff1 fs2 fc0 sc0 ls0 ws0">in<span class="_ _11"> </span>reducing<span class="_ _13"> </span>noise<span class="_ _13"> </span>while<span class="_ _13"> </span>retaining<span class="_ _11"> </span>image<span class="_ _13"> </span>details.<span class="_ _13"> </span>The<span class="_ _13"> </span>signif-</div><div class="t m0 x4 h5 y1f ff1 fs2 fc0 sc0 ls0 ws0">icant<span class="_ _13"> </span>work<span class="_ _6"> </span>on<span class="_ _6"> </span>signal<span class="_ _6"> </span>denoising<span class="_ _6"> </span>via<span class="_ _6"> </span><span class="ff4">wav<span class="_ _7"></span>elet<span class="_ _8"> </span>thresholding<span class="_ _5"> </span><span class="ff1">or</span></span></div><div class="t m0 x4 h5 y20 ff4 fs2 fc0 sc0 ls0 ws0">shrinkage<span class="_ _e"> </span><span class="ff1">of<span class="_"> </span>Donoho<span class="_"> </span>and<span class="_ _d"> </span>Johnstone<span class="_"> </span>[3]<span class="_ _d"> </span>has<span class="_ _d"> </span>shown<span class="_"> </span>that<span class="_"> </span>various</span></div><div class="t m0 x4 h5 y21 ff1 fs2 fc0 sc0 ls0 ws0">wa<span class="_ _7"></span>velet<span class="_ _e"> </span>thresholding<span class="_ _8"> </span>schemes<span class="_ _8"> </span>for<span class="_ _e"> </span>denoising<span class="_ _8"> </span>hav<span class="_ _7"></span>e<span class="_ _8"> </span>nearoptimal</div><div class="t m0 x4 h5 y22 ff1 fs2 fc0 sc0 ls0 ws0">properties<span class="_"> </span>in<span class="_"> </span>the<span class="_"> </span>minimax<span class="_"> </span>sense<span class="_ _c"> </span>and<span class="_"> </span>perform<span class="_"> </span>well<span class="_ _c"> </span>in<span class="_"> </span>simulation</div><div class="t m0 x4 h5 y23 ff1 fs2 fc0 sc0 ls0 ws0">studies<span class="_ _e"> </span>of<span class="_ _e"> </span>one-dimensional<span class="_ _8"> </span>curve<span class="_ _e"> </span>estimation<span class="_ _e"> </span>[2].</div><div class="t m0 x8 h5 y24 ff1 fs2 fc0 sc0 ls0 ws0">Begin<span class="_ _9"> </span>with<span class="_ _9"> </span>Donoho<span class="_ _9"> </span>and<span class="_ _9"> </span>Johnstones<span class="_ _9"> </span>w<span class="_ _7"></span>av<span class="_ _7"></span>elet<span class="_ _9"> </span>coef&#64257;cient</div><div class="t m0 x4 h5 y25 ff1 fs2 fc0 sc0 ls0 ws0">shrinking(<span class="ff4">wa<span class="_ _7"></span>velet<span class="_ _14"> </span>thresholding<span class="_ _15"></span><span class="ff1">),<span class="_"> </span>in<span class="_"> </span>[1]<span class="_ _c"> </span>they<span class="_ _c"> </span>proposed<span class="_"> </span>a<span class="_ _c"> </span>wa<span class="_ _1"></span>velet</span></span></div><div class="t m0 x4 h5 y26 ff1 fs2 fc0 sc0 ls0 ws0">denosing<span class="_ _8"> </span>scheme<span class="_ _8"> </span>by<span class="_ _8"> </span>using<span class="_ _b"> </span>soft<span class="_ _8"> </span>thresholding<span class="_ _8"> </span>and<span class="_ _b"> </span>hard<span class="_ _8"> </span>thresh-</div><div class="t m0 x4 h5 y27 ff1 fs2 fc0 sc0 ls0 ws0">olding.<span class="_"> </span>This<span class="_ _d"> </span>method<span class="_ _d"> </span>performs<span class="_ _d"> </span>well<span class="_ _d"> </span>in<span class="_ _d"> </span>image<span class="_ _d"> </span>denoising<span class="_ _d"> </span>because</div><div class="t m0 x4 h5 y28 ff1 fs2 fc0 sc0 ls0 ws0">wa<span class="_ _7"></span>velet<span class="_ _12"> </span>transform<span class="_ _12"> </span>has<span class="_ _12"> </span>the<span class="_ _12"> </span>compaction<span class="_ _12"> </span>property<span class="_ _12"> </span>of<span class="_ _e"> </span>ha<span class="_ _7"></span>ving<span class="_ _12"> </span>only</div><div class="t m0 x4 h5 y29 ff1 fs2 fc0 sc0 ls0 ws0">a<span class="_ _11"> </span>small<span class="_ _11"> </span>number<span class="_ _11"> </span>of<span class="_ _11"> </span>large<span class="_ _11"> </span>coef<span class="_ _7"></span>&#64257;cients.<span class="_ _11"> </span>The<span class="_ _11"> </span>denoising<span class="_ _11"> </span>is<span class="_ _11"> </span>done</div><div class="t m0 x4 h5 y2a ff1 fs2 fc0 sc0 ls0 ws0">only<span class="_ _6"> </span>on<span class="_ _16"> </span>the<span class="_ _6"> </span>detail<span class="_ _16"> </span>coef<span class="_ _7"></span>&#64257;cients<span class="_ _16"> </span>of<span class="_ _6"> </span>the<span class="_ _16"> </span>wa<span class="_ _1"></span>velet<span class="_ _6"> </span>transform.<span class="_ _16"> </span>It</div><div class="t m0 x4 h5 y2b ff1 fs2 fc0 sc0 ls0 ws0">has<span class="_ _11"> </span>been<span class="_ _11"> </span>sho<span class="_ _7"></span>wn<span class="_ _11"> </span>that<span class="_ _11"> </span>this<span class="_ _11"> </span>algorithm<span class="_ _11"> </span>of<span class="_ _7"></span>fers<span class="_ _11"> </span>the<span class="_ _11"> </span>adv<span class="_ _7"></span>antages<span class="_ _11"> </span>of</div><div class="t m0 x4 h5 y2c ff1 fs2 fc0 sc0 ls0 ws0">smoothness<span class="_ _9"> </span>and<span class="_ _9"> </span>adaptation<span class="_ _5"> </span>[4].<span class="_ _9"> </span>Howe<span class="_ _1"></span>ver<span class="_ _7"></span>,<span class="_ _9"> </span>as<span class="_ _9"> </span>Coifamn<span class="_ _9"> </span>and</div><div class="t m0 x4 h5 y2d ff1 fs2 fc0 sc0 ls0 ws0">Donoho<span class="_"> </span>[5]<span class="_"> </span>pointed<span class="_"> </span>out,<span class="_"> </span>this<span class="_"> </span>algorithm<span class="_"> </span>exhibits<span class="_"> </span>visual<span class="_"> </span>artifacts:</div><div class="t m0 x4 h5 y2e ff1 fs2 fc0 sc0 ls0 ws0">Gibbs<span class="_ _e"> </span>phenomena<span class="_ _e"> </span>in<span class="_ _8"> </span>the<span class="_ _e"> </span>neighbourhood<span class="_ _8"> </span>of<span class="_ _e"> </span>discontinuities.</div><div class="t m0 x8 h5 y2f ff1 fs2 fc0 sc0 ls0 ws0">Unlike<span class="_ _e"> </span>early<span class="_ _e"> </span>simple<span class="_ _e"> </span>hard<span class="_ _e"> </span>thresholding<span class="_ _e"> </span>or<span class="_ _e"> </span>soft<span class="_ _e"> </span>thresholding</div><div class="t m0 x4 h5 y30 ff1 fs2 fc0 sc0 ls0 ws0">in<span class="_ _16"> </span>[4],<span class="_ _16"> </span>most<span class="_ _9"> </span>recently<span class="_ _16"> </span>algorithms<span class="_ _16"> </span>are<span class="_ _9"> </span>based<span class="_ _16"> </span>on<span class="_ _9"> </span>Bayes<span class="_ _16"> </span>rule.</div><div class="t m0 x4 h5 y31 ff1 fs2 fc0 sc0 ls0 ws0">In<span class="_ _5"> </span>Bayes<span class="_ _5"> </span>based<span class="_ _3"> </span>models,<span class="_ _5"> </span>we<span class="_ _3"> </span>need<span class="_ _5"> </span>a<span class="_ _3"> </span>probability<span class="_ _5"> </span>model<span class="_ _3"> </span>to</div><div class="t m0 x4 h5 y32 ff1 fs2 fc0 sc0 ls0 ws0">describe<span class="_ _16"> </span>the<span class="_ _16"> </span>distribution<span class="_ _16"> </span>of<span class="_ _16"> </span>noise<span class="_ _16"> </span>free<span class="_ _16"> </span>wa<span class="_ _1"></span>velet<span class="_ _16"> </span>coef&#64257;cients.</div><div class="t m0 x4 h5 y33 ff1 fs2 fc0 sc0 ls0 ws0">In<span class="_ _11"> </span>this<span class="_ _b"> </span>paper,<span class="_ _b"> </span>we<span class="_ _11"> </span>implement<span class="_ _b"> </span>two<span class="_ _11"> </span>kinds<span class="_ _11"> </span>of<span class="_ _b"> </span>wav<span class="_ _7"></span>elet<span class="_ _11"> </span>shrinking</div><div class="t m0 x9 h5 y3 ff1 fs2 fc0 sc0 ls0 ws0">methods:<span class="_ _b"> </span>V<span class="_ _1"></span>iruShrink<span class="_ _11"> </span>[1]<span class="_ _11"> </span>and<span class="_ _b"> </span>BayesShrink<span class="_ _11"> </span>[2].<span class="_ _11"> </span>V<span class="_ _1"></span>iruShrink<span class="_ _b"> </span>is</div><div class="t m0 x9 h5 y34 ff1 fs2 fc0 sc0 ls0 ws0">a<span class="_ _e"> </span>simple<span class="_ _e"> </span>method<span class="_ _e"> </span>to<span class="_ _8"> </span>get<span class="_ _e"> </span>a<span class="_ _e"> </span>univ<span class="_ _7"></span>ersal<span class="_ _e"> </span>threshold<span class="_ _e"> </span>for<span class="_ _8"> </span>all<span class="_ _e"> </span>the<span class="_ _e"> </span>detail</div><div class="t m0 x9 h5 y35 ff1 fs2 fc0 sc0 ls0 ws0">coef&#64257;cients.<span class="_ _12"> </span>Howe<span class="_ _7"></span>ver<span class="_ _1"></span>,<span class="_ _e"> </span>BayesShrink<span class="_ _8"> </span>is<span class="_ _e"> </span>an<span class="_ _e"> </span>adaptiv<span class="_ _7"></span>e<span class="_ _e"> </span>data-driv<span class="_ _7"></span>en</div><div class="t m0 x9 h5 y36 ff1 fs2 fc0 sc0 ls0 ws0">method<span class="_ _12"> </span>and<span class="_ _e"> </span>the<span class="_ _12"> </span>corresponding<span class="_ _e"> </span>threshold<span class="_ _12"> </span>is<span class="_ _e"> </span>simple<span class="_ _12"> </span>and<span class="_ _e"> </span>colsed-</div><div class="t m0 x9 h5 y37 ff1 fs2 fc0 sc0 ls0 ws0">form<span class="_ _11"> </span>and<span class="_ _11"> </span>it<span class="_ _11"> </span>is<span class="_ _13"> </span>adapti<span class="_ _7"></span>ve<span class="_ _11"> </span>to<span class="_ _11"> </span>each<span class="_ _11"> </span>subband<span class="_ _11"> </span>because<span class="_ _11"> </span>it<span class="_ _11"> </span>depends</div><div class="t m0 x9 h5 y38 ff1 fs2 fc0 sc0 ls0 ws0">on<span class="_ _11"> </span>data-dri<span class="_ _7"></span>ven<span class="_ _b"> </span>estimates<span class="_ _11"> </span>of<span class="_ _11"> </span>the<span class="_ _11"> </span>parameters.<span class="_ _11"> </span>The<span class="_ _11"> </span>threshold<span class="_ _11"> </span>is</div><div class="t m0 x9 h5 y39 ff1 fs2 fc0 sc0 ls0 ws0">deriv<span class="_ _1"></span>ed<span class="_ _13"> </span>in<span class="_ _6"> </span>a<span class="_ _13"> </span>Batesian<span class="_ _13"> </span>framew<span class="_ _7"></span>ork<span class="_ _13"> </span>and<span class="_ _13"> </span>the<span class="_ _13"> </span>probability<span class="_ _13"> </span>model</div><div class="t m0 x9 h5 y3a ff1 fs2 fc0 sc0 ls0 ws0">used<span class="_ _11"> </span>on<span class="_ _11"> </span>the<span class="_ _b"> </span>wavelet<span class="_ _b"> </span>coef&#64257;cients<span class="_ _b"> </span>is<span class="_ _11"> </span>the<span class="_ _11"> </span>generalized<span class="_ _11"> </span>Gaussian</div><div class="t m0 x9 h5 y3b ff1 fs2 fc0 sc0 ls0 ws0">distribution(GGD).</div><div class="t m0 xa h5 y3c ff1 fs2 fc0 sc0 ls0 ws0">This<span class="_ _12"> </span>paper<span class="_ _12"> </span>is<span class="_ _e"> </span>org<span class="_ _7"></span>anized<span class="_ _12"> </span>as<span class="_ _e"> </span>follo<span class="_ _7"></span>w:<span class="_ _12"> </span>in<span class="_ _e"> </span>Section<span class="_ _12"> </span>II,<span class="_ _12"> </span>we<span class="_ _12"> </span>brie&#64258;y</div><div class="t m0 x9 h5 y3d ff1 fs2 fc0 sc0 ls0 ws0">introduce<span class="_ _b"> </span>the<span class="_ _8"> </span>basic<span class="_ _b"> </span>of<span class="_ _b"> </span>wav<span class="_ _7"></span>elet<span class="_ _b"> </span>thresholding<span class="_ _b"> </span>image<span class="_ _b"> </span>denoising.</div><div class="t m0 x9 h5 y3e ff1 fs2 fc0 sc0 ls0 ws0">The<span class="_ _e"> </span>concrete<span class="_ _8"> </span>descriptions<span class="_ _e"> </span>of<span class="_ _8"> </span>V<span class="_ _1"></span>iruShrink<span class="_ _e"> </span>and<span class="_ _8"> </span>BayesShrink<span class="_ _e"> </span>are</div><div class="t m0 x9 h5 y3f ff1 fs2 fc0 sc0 ls0 ws0">shown<span class="_ _12"> </span>in<span class="_ _e"> </span>Section<span class="_ _e"> </span>III.<span class="_ _e"> </span>In<span class="_ _e"> </span>Section<span class="_ _8"> </span>IV,<span class="_ _e"> </span>experimental<span class="_ _12"> </span>results<span class="_ _e"> </span>give</div><div class="t m0 x9 h5 y40 ff1 fs2 fc0 sc0 ls0 ws0">comparisons<span class="_"> </span>of<span class="_ _d"> </span>PSNR<span class="_ _d"> </span>[6]<span class="_ _d"> </span>between<span class="_ _d"> </span>these<span class="_ _d"> </span>two<span class="_"> </span>methods.<span class="_ _d"> </span>W<span class="_ _4"></span>e<span class="_ _d"> </span>will</div><div class="t m0 x9 h5 y41 ff1 fs2 fc0 sc0 ls0 ws0">show<span class="_ _12"> </span>the<span class="_ _e"> </span>denoising<span class="_ _e"> </span>performance<span class="_ _8"> </span>on<span class="_ _e"> </span>dif<span class="_ _7"></span>ferent<span class="_ _e"> </span>conditions,<span class="_ _e"> </span>such</div><div class="t m0 x9 h5 y42 ff1 fs2 fc0 sc0 ls0 ws0">as<span class="_ _e"> </span>dif<span class="_ _7"></span>ferent<span class="_ _e"> </span>grey<span class="_ _12"> </span>images,<span class="_ _e"> </span>different<span class="_ _e"> </span>wa<span class="_ _1"></span>velet<span class="_ _e"> </span>functions,<span class="_ _e"> </span>dif<span class="_ _7"></span>ferent</div><div class="t m0 x9 h5 y43 ff1 fs2 fc0 sc0 ls0 ws0">variance<span class="_ _d"> </span>of<span class="_ _12"> </span>Gaussian<span class="_ _12"> </span>noise,<span class="_ _e"> </span>etc.<span class="_ _12"> </span>Finally<span class="_ _4"></span>,<span class="_ _12"> </span>we<span class="_ _12"> </span>draw<span class="_ _12"> </span>a<span class="_ _12"> </span>conclusion</div><div class="t m0 x9 h5 y44 ff1 fs2 fc0 sc0 ls0 ws0">in<span class="_ _e"> </span>Section<span class="_ _e"> </span>V.</div><div class="t m0 xb h5 y45 ff1 fs2 fc0 sc0 ls0 ws0">I<span class="_ _f"></span>I<span class="_ _f"></span>.<span class="_ _10"> </span>W<span class="_ _1"></span><span class="fs3">A<span class="_ _1"></span>V<span class="_ _f"></span>E<span class="_ _f"></span>L<span class="_ _f"></span>E<span class="_ _f"></span>T<span class="_ _12"> </span><span class="fs2">S<span class="_ _f"></span></span>H<span class="_ _f"></span>R<span class="_ _f"></span>I<span class="_ _f"></span>N<span class="_ _f"></span>K<span class="_ _f"></span>I<span class="_ _f"></span>N<span class="_ _f"></span>G</span></div><div class="t m0 xa h5 y46 ff1 fs2 fc0 sc0 ls0 ws0">In<span class="_ _b"> </span>this<span class="_ _b"> </span>section,<span class="_ _b"> </span>we<span class="_ _11"> </span>will<span class="_ _b"> </span>discuss<span class="_ _b"> </span>the<span class="_ _b"> </span>basic<span class="_ _b"> </span>idea<span class="_ _11"> </span>of<span class="_ _8"> </span>wavelet</div><div class="t m0 x9 h7 y47 ff1 fs2 fc0 sc0 ls0 ws0">shrinking.<span class="_ _11"> </span>Let<span class="_ _13"> </span>the<span class="_ _11"> </span>signal<span class="_ _13"> </span>be<span class="_ _11"> </span><span class="ff5">f</span></div><div class="t m0 xc h8 y48 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 xd h7 y47 ff5 fs2 fc0 sc0 ls0 ws0">,<span class="_ _14"> </span>i<span class="_ _11"> </span><span class="ff7">=<span class="_ _13"> </span>1</span>,<span class="_ _14"> </span><span class="ff8">&#183;<span class="_ _14"></span>&#183;<span class="_ _17"></span>&#183;<span class="_ _e"> </span></span>,<span class="_ _17"> </span>N<span class="_ _17"> </span><span class="ff1">,<span class="_ _11"> </span>where<span class="_ _11"> </span></span>N<span class="_ _9"> </span><span class="ff1">is</span></div><div class="t m0 x9 h5 y49 ff1 fs2 fc0 sc0 ls0 ws0">some<span class="_ _11"> </span>integer<span class="_ _11"> </span>power<span class="_ _11"> </span>of<span class="_ _13"> </span>2.<span class="_ _11"> </span>It<span class="_ _13"> </span>has<span class="_ _11"> </span>been<span class="_ _13"> </span>corrupted<span class="_ _13"> </span>by<span class="_ _11"> </span>additiv<span class="_ _7"></span>e</div><div class="t m0 x9 h5 y4a ff1 fs2 fc0 sc0 ls0 ws0">Gaussian<span class="_ _e"> </span>noise<span class="_ _e"> </span>and<span class="_ _8"> </span>one<span class="_ _e"> </span>observes</div><div class="t m0 xe h7 y4b ff5 fs2 fc0 sc0 ls0 ws0">g</div><div class="t m0 xf h8 y4c ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x10 h7 y4b ff7 fs2 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff5">f</span></div><div class="t m0 x11 h8 y4c ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x12 h7 y4b ff7 fs2 fc0 sc0 ls0 ws0">+<span class="_ _c"> </span><span class="ff5">&#949;</span></div><div class="t m0 x13 h8 y4c ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x14 h7 y4b ff5 fs2 fc0 sc0 ls0 ws0">,<span class="_ _17"> </span>i,<span class="_ _14"> </span>j<span class="_ _e"> </span><span class="ff7">=<span class="_"> </span>1</span>,<span class="_ _17"> </span><span class="ff8">&#183;<span class="_ _14"></span>&#183;<span class="_ _17"></span>&#183;<span class="_ _e"> </span></span>,<span class="_ _14"> </span>N<span class="_ _18"> </span><span class="ff1">(1)</span></div><div class="t m0 x9 h7 y4d ff1 fs2 fc0 sc0 ls0 ws0">where<span class="_ _8"> </span><span class="ff5">&#949;</span></div><div class="t m0 x15 h8 y4e ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x16 h5 y4d ff1 fs2 fc0 sc0 ls0 ws0">are<span class="_ _8"> </span>independent<span class="_ _b"> </span>and<span class="_ _8"> </span>identically<span class="_ _b"> </span>distributed<span class="_ _8"> </span>(iid)<span class="_ _b"> </span>as</div><div class="t m0 x9 h7 y4f ff1 fs2 fc0 sc0 ls0 ws0">normal<span class="_"> </span><span class="ff5">N<span class="_ _19"></span><span class="ff7">(0</span>,<span class="_ _17"> </span>&#963;</span></div><div class="t m0 x17 h9 y50 ff9 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x18 h7 y4f ff7 fs2 fc0 sc0 ls0 ws0">)<span class="_ _c"> </span><span class="ff1">and<span class="_"> </span>independent<span class="_"> </span>of<span class="_"> </span><span class="ff5">f</span></span></div><div class="t m0 x19 h8 y51 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x1a h5 y4f ff1 fs2 fc0 sc0 ls0 ws0">.<span class="_"> </span>The<span class="_"> </span>goal<span class="_"> </span>is<span class="_"> </span>to<span class="_"> </span>remov<span class="_ _1"></span>e</div><div class="t m0 x9 h7 y52 ff1 fs2 fc0 sc0 ls0 ws0">the<span class="_ _e"> </span>noise<span class="_ _e"> </span>from<span class="_ _8"> </span><span class="ff5">g</span></div><div class="t m0 x1b h8 y53 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x1c h5 y52 ff1 fs2 fc0 sc0 ls0 ws0">and<span class="_ _e"> </span>to<span class="_ _e"> </span>obtain<span class="_ _8"> </span>an<span class="_ _e"> </span>estimate</div><div class="t m0 x1d h7 y54 ff7 fs2 fc0 sc0 ls0 ws0">&#710;</div><div class="t m0 x1e h7 y52 ff5 fs2 fc0 sc0 ls0 ws0">f</div><div class="t m0 x1f h8 y53 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x20 h7 y52 ff1 fs2 fc0 sc0 ls0 ws0">of<span class="_ _e"> </span><span class="ff5">f</span></div><div class="t m0 x21 h8 y53 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x22 h5 y52 ff1 fs2 fc0 sc0 ls0 ws0">which</div><div class="t m0 x9 h5 y55 ff1 fs2 fc0 sc0 ls0 ws0">minimizes<span class="_ _e"> </span>the<span class="_ _e"> </span>mean<span class="_ _8"> </span>squared<span class="_ _e"> </span>error<span class="_ _8"> </span>[6]<span class="_ _e"> </span>(MSE,<span class="_ _e"> </span>shown<span class="_ _e"> </span>in<span class="_ _e"> </span>Eq.<span class="_ _8"> </span>),</div><div class="t m0 x23 h7 y56 ff5 fs2 fc0 sc0 ls0 ws0">M<span class="_ _19"></span>S<span class="_ _f"></span>E<span class="_ _f"></span><span class="ff7">(</span></div><div class="t m0 x24 h7 y57 ff7 fs2 fc0 sc0 ls0 ws0">&#710;</div><div class="t m0 x24 h7 y56 ffa fs2 fc0 sc0 ls0 ws0">f<span class="_ _19"></span><span class="ff7">)<span class="_"> </span>=</span></div><div class="t m0 x25 h7 y58 ff7 fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 x26 h7 y59 ff5 fs2 fc0 sc0 ls0 ws0">N</div><div class="t m0 x27 h9 y5a ff9 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 xd h8 y5b ff6 fs5 fc0 sc0 ls0 ws0">N</div><div class="t m0 x28 ha y5c ffb fs2 fc0 sc0 ls0 ws0">X</div><div class="t m0 xc h8 y5d ff6 fs5 fc0 sc0 ls0 ws0">i,j<span class="_ _f"></span><span class="ff9">=1</span></div><div class="t m0 x29 h7 y56 ff7 fs2 fc0 sc0 ls0 ws0">(</div><div class="t m0 x2a h7 y57 ff7 fs2 fc0 sc0 ls0 ws0">&#710;</div><div class="t m0 x2b h7 y56 ff5 fs2 fc0 sc0 ls0 ws0">f</div><div class="t m0 x2c h8 y5e ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x2d h7 y56 ff8 fs2 fc0 sc0 ls0 ws0">&#8722;<span class="_ _c"> </span><span class="ff5">f</span></div><div class="t m0 x2e h8 y5e ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x1e h7 y56 ff7 fs2 fc0 sc0 ls0 ws0">)</div><div class="t m0 x2f h9 y5f ff9 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x30 h5 y56 ff1 fs2 fc0 sc0 ls0 ws0">(2)</div><div class="t m0 xa h7 y60 ff1 fs2 fc0 sc0 ls0 ws0">Let<span class="_ _11"> </span><span class="ffa">g<span class="_ _16"> </span><span class="ff7">=<span class="_ _13"> </span>(<span class="ff5">g</span></span></span></div><div class="t m0 x18 h8 y61 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x31 h7 y60 ff7 fs2 fc0 sc0 ls0 ws0">)</div><div class="t m0 x32 h8 y61 ff6 fs5 fc0 sc0 ls0 ws0">i,j</div><div class="t m0 x33 h7 y60 ff5 fs2 fc0 sc0 ls0 ws0">,<span class="_ _17"> </span><span class="ffa">f<span class="_ _5"> </span><span class="ff7">=<span class="_ _13"> </span>(</span></span>f</div><div class="t m0 x27 h8 y61 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 xc h7 y60 ff7 fs2 fc0 sc0 ls0 ws0">)</div><div class="t m0 x34 h8 y61 ff6 fs5 fc0 sc0 ls0 ws0">i,j</div><div class="t m0 x35 h7 y60 ff1 fs2 fc0 sc0 ls0 ws0">,<span class="_ _11"> </span>and<span class="_ _13"> </span><span class="ff5">&#949;<span class="_ _6"> </span><span class="ff7">=<span class="_ _13"> </span>(</span>&#949;</span></div><div class="t m0 x36 h8 y61 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x37 h7 y60 ff7 fs2 fc0 sc0 ls0 ws0">)</div><div class="t m0 x38 h8 y61 ff6 fs5 fc0 sc0 ls0 ws0">i,j</div><div class="t m0 x39 h5 y60 ff1 fs2 fc0 sc0 ls0 ws0">,<span class="_ _11"> </span>that<span class="_ _13"> </span>is,</div><div class="t m0 x9 h5 y62 ff1 fs2 fc0 sc0 ls0 ws0">the<span class="_ _8"> </span>boldfaced<span class="_ _b"> </span>letters<span class="_ _b"> </span>will<span class="_ _b"> </span>denote<span class="_ _b"> </span>the<span class="_ _8"> </span>matrix<span class="_ _b"> </span>representation<span class="_ _b"> </span>of</div><div class="t m0 x9 h7 y63 ff1 fs2 fc0 sc0 ls0 ws0">the<span class="_ _16"> </span>signals<span class="_ _6"> </span>under<span class="_ _16"> </span>consideration.<span class="_ _6"> </span>Let<span class="_ _16"> </span><span class="ffa">Y<span class="_ _3"> </span><span class="ff7">=<span class="_ _5"> </span><span class="ff8">W<span class="_ _15"></span></span></span>g<span class="_ _16"> </span></span>denote<span class="_ _16"> </span>the</div><div class="t m0 x9 h7 y64 ff1 fs2 fc0 sc0 ls0 ws0">matrix<span class="_ _16"> </span>of<span class="_ _16"> </span>wa<span class="_ _1"></span>velet<span class="_ _16"> </span>coef&#64257;cients<span class="_ _6"> </span>of<span class="_ _16"> </span><span class="ffa">g<span class="_"> </span></span>,<span class="_ _16"> </span>where<span class="_ _16"> </span><span class="ff8">W<span class="_ _3"> </span></span>is<span class="_ _16"> </span>the<span class="_ _16"> </span>two-</div><div class="t m0 x9 h5 y65 ff1 fs2 fc0 sc0 ls0 ws0">dimensional<span class="_"> </span>dyadic<span class="_"> </span>orthogonal<span class="_"> </span>wa<span class="_ _1"></span>velet<span class="_"> </span>transform<span class="_"> </span>operator<span class="_ _1"></span>,<span class="_"> </span>and</div><div class="t m0 x9 h7 y66 ff1 fs2 fc0 sc0 ls0 ws0">similarly<span class="_ _11"> </span><span class="ffa">X<span class="_ _11"> </span><span class="ff7">=<span class="_ _13"> </span><span class="ff8">W<span class="_ _15"></span></span></span>f<span class="_ _9"> </span></span>and<span class="_ _11"> </span><span class="ffa">V<span class="_ _13"> </span><span class="ff7">=<span class="_ _11"> </span><span class="ff8">W<span class="_ _19"></span><span class="ff5">&#949;</span></span></span></span>.<span class="_ _11"> </span>It<span class="_ _11"> </span>is<span class="_ _13"> </span>con<span class="_ _1"></span>venient<span class="_ _11"> </span>to<span class="_ _11"> </span>label</div><div class="t m0 x9 h5 y67 ff1 fs2 fc0 sc0 ls0 ws0">the<span class="_ _9"> </span>subbands<span class="_ _9"> </span>of<span class="_ _5"> </span>the<span class="_ _9"> </span>transform<span class="_ _5"> </span>as<span class="_ _9"> </span>in<span class="_ _9"> </span>Fig.1.<span class="_ _5"> </span>The<span class="_ _9"> </span>subbands</div><div class="t m0 x9 h7 y68 ff5 fs2 fc0 sc0 ls0 ws0">H<span class="_ _15"></span>H</div><div class="t m0 x3a h8 y69 ff6 fs5 fc0 sc0 ls0 ws0">k</div><div class="t m0 x3b h7 y68 ff5 fs2 fc0 sc0 ls0 ws0">,<span class="_ _17"> </span>H<span class="_ _19"></span>L</div><div class="t m0 x3c h8 y69 ff6 fs5 fc0 sc0 ls0 ws0">k</div><div class="t m0 x3d h7 y68 ff5 fs2 fc0 sc0 ls0 ws0">,<span class="_ _17"> </span>LH</div><div class="t m0 xf h8 y69 ff6 fs5 fc0 sc0 ls0 ws0">k</div><div class="t m0 x3e h7 y68 ff5 fs2 fc0 sc0 ls0 ws0">,<span class="_ _17"> </span>k<span class="_ _0"> </span><span class="ff7">=<span class="_ _0"> </span>1</span>,<span class="_ _17"> </span><span class="ff7">2</span>,<span class="_ _17"> </span><span class="ff8">&#183;<span class="_ _14"></span>&#183;<span class="_ _17"></span>&#183;<span class="_ _e"> </span></span>,<span class="_ _14"> </span>J<span class="_ _1a"> </span><span class="ff1">are<span class="_ _3"> </span>called<span class="_ _a"> </span>the<span class="_ _3"> </span><span class="ff4">details</span>,</span></div><div class="t m0 x9 h7 y6a ff1 fs2 fc0 sc0 ls0 ws0">where<span class="_ _13"> </span><span class="ff5">k<span class="_ _6"> </span></span>is<span class="_ _13"> </span>the<span class="_ _13"> </span><span class="ff4">scale</span>,<span class="_ _13"> </span>with<span class="_ _13"> </span><span class="ff5">J<span class="_ _5"> </span></span>being<span class="_ _13"> </span>the<span class="_ _13"> </span>largest<span class="_ _11"> </span>scale<span class="_ _6"> </span>in<span class="_ _13"> </span>the</div><div class="t m0 x9 h7 y6b ff1 fs2 fc0 sc0 ls0 ws0">decomposition,<span class="_"> </span>and<span class="_ _c"> </span>a<span class="_ _c"> </span>subband<span class="_ _c"> </span>at<span class="_ _c"> </span>scale<span class="_"> </span><span class="ff5">k<span class="_ _c"> </span></span>has<span class="_"> </span>size<span class="_"> </span><span class="ff5">N/<span class="ff7">2</span></span></div><div class="t m0 x3f h8 y6c ff6 fs5 fc0 sc0 ls0 ws0">k</div><div class="t m0 x40 h7 y6b ff8 fs2 fc0 sc0 ls0 ws0">&#215;<span class="ff5">N<span class="_ _f"></span>/<span class="ff7">2</span></span></div><div class="t m0 x41 h8 y6c ff6 fs5 fc0 sc0 ls0 ws0">k</div><div class="t m0 x42 h5 y6b ff1 fs2 fc0 sc0 ls0 ws0">.</div><div class="t m0 x9 h7 y6d ff1 fs2 fc0 sc0 ls0 ws0">The<span class="_ _6"> </span>subband<span class="_ _6"> </span><span class="ff5">LL</span></div><div class="t m0 x3e h8 y6e ff6 fs5 fc0 sc0 ls0 ws0">J</div><div class="t m0 x43 h7 y6d ff1 fs2 fc0 sc0 ls0 ws0">is<span class="_ _6"> </span>the<span class="_ _6"> </span>low<span class="_ _13"> </span>resolution<span class="_ _6"> </span>residual,<span class="_ _6"> </span>and<span class="_ _6"> </span><span class="ff5">J<span class="_ _5"> </span></span>is</div><div class="t m0 x9 h7 y6f ff1 fs2 fc0 sc0 ls0 ws0">typically<span class="_ _16"> </span>chosen<span class="_ _16"> </span>large<span class="_ _16"> </span>enough<span class="_ _16"> </span>such<span class="_ _16"> </span>that<span class="_ _16"> </span><span class="ff5">N<span class="_ _f"></span>/<span class="ff7">2</span></span></div><div class="t m0 x44 h8 y70 ff6 fs5 fc0 sc0 ls0 ws0">J</div><div class="t m0 x38 h7 y6f ff8 fs2 fc0 sc0 ls0 ws0">&#58908;<span class="_ _3"> </span><span class="ff5">N<span class="_"> </span><span class="ff1">and</span></span></div><div class="t m0 x9 h7 y71 ff5 fs2 fc0 sc0 ls0 ws0">N<span class="_ _f"></span>/<span class="ff7">2</span></div><div class="t m0 x45 h8 y72 ff6 fs5 fc0 sc0 ls0 ws0">J</div><div class="t m0 x46 h7 y71 ff5 fs2 fc0 sc0 ls0 ws0">&gt;<span class="_ _b"> </span><span class="ff7">1<span class="ff1">.<span class="_ _11"> </span>Note<span class="_ _11"> </span>that<span class="_ _11"> </span>since<span class="_ _b"> </span>the<span class="_ _11"> </span>transform<span class="_ _11"> </span>is<span class="_ _11"> </span>orthogonal,<span class="_ _11"> </span></span></span>V</div><div class="t m0 x41 h8 y73 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x9 h7 y74 ff1 fs2 fc0 sc0 ls0 ws0">are<span class="_ _e"> </span>also<span class="_ _e"> </span><span class="ff4">idd<span class="_ _13"> </span><span class="ff5">N<span class="_ _19"> </span><span class="ff7">(0</span>,<span class="_ _14"> </span>&#963;</span></span></div><div class="t m0 x47 h9 y75 ff9 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x48 h7 y74 ff7 fs2 fc0 sc0 ls0 ws0">)<span class="ff1">.</span></div><div class="t m0 xa h5 y32 ff1 fs2 fc0 sc0 ls0 ws0">The<span class="_ _9"> </span>wav<span class="_ _7"></span>elet-thresholding<span class="_ _9"> </span>denoising<span class="_ _5"> </span>method<span class="_ _9"> </span>&#64257;lters<span class="_ _5"> </span>each</div><div class="t m0 x9 h7 y33 ff1 fs2 fc0 sc0 ls0 ws0">coef&#64257;cient<span class="_ _9"> </span><span class="ff5">Y</span></div><div class="t m0 x49 h8 y76 ff6 fs5 fc0 sc0 ls0 ws0">ij</div><div class="t m0 xf h5 y33 ff1 fs2 fc0 sc0 ls0 ws0">from<span class="_ _5"> </span>the<span class="_ _5"> </span>detail<span class="_ _5"> </span>subbands<span class="_ _5"> </span>with<span class="_ _5"> </span>a<span class="_ _5"> </span>threshold</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
评论
    相关推荐
    • Feature_Extraction小波去噪.zip
      用Python实现小波去噪和特征提取,语法简练,可以直接使用
    • 小波去噪.rar
      小波去噪的ViruShrink和BayesShrink算法实现,含源代码及LaTeX报告
    • DeNoising.rar
      几种小波变换去噪的算法,可以运行在win2000,和XP。
    • 小波去噪 MATLAB
      利用小波分解对含噪声图像进行阈值去噪,重构得到新图像。将图像分解后的高频部分的振幅进行软阈值去噪 ,并将试验结果与实数小波去噪结果相比较。结果表明该方法既能有效地去除噪声 ,又能保持图像的大量原始信息
    • 小波阈值去噪MATLAB代码-wdenoise:小波去噪
      小波阈值去噪MATLAB代码瓦迪诺斯 使用经验贝叶斯阈值和许多其他阈值方法在ANSI C中进行小波消噪。 WDenoise对象,参数和函数 示例代码1:wdenoise(EBayesThresh) 示例代码2:wdenoise 示例代码3:使用EBayesThresh...
    • 维纳滤波音频去噪matlab代码-wavelet-denoising:基于多谱谱自适应小波去噪的语音增强
      维纳滤波音频去噪matlab代码小波去噪 基于多锥谱自适应小波去噪的Yu和Guizou语音增强的Matlab实现。 布雷西亚大学信息表示高级方法课程的最终项目,2018年。 众所周知,在大多数频域语音增强算法中遇到的“音乐噪声...
    • 小波去噪和边缘增强.
      本程序由MATLAB开发,可以对图像进行小波去噪和边缘增强
    • 小波去噪MATLAB程序
      小波去噪的应用,Read me This is tool that is constructed for wavelet denoising, please put reference of your Matlab current directory to this directory. Important I have tested this code only in ...
    • BayesWavelet小波去噪
      BayesWavelet 小波去噪用matlab实现
    • codesforimageprocessing.rar
      实现简单图像处理,包括256色转灰度图、Hough变换、Walsh变换、中值滤波、二值化变换、亮度增减、傅立叶变换、反色、取对数、取指数、图像平移、图像旋转、图像细化、图像缩放、图像镜像、均值滤波、对比度拉伸、拉普拉斯锐化(边缘检测)、方块编码、梯度锐化、灰度均衡、直方图均衡、离散余弦变换、维纳滤波处理、逆滤波处理、阈值变换、高斯平滑。