{"id":11686,"date":"2021-06-24T13:34:44","date_gmt":"2021-06-24T10:34:44","guid":{"rendered":"https:\/\/umram.bilkent.edu.tr\/?p=11686"},"modified":"2021-06-24T13:34:44","modified_gmt":"2021-06-24T10:34:44","slug":"umramdan-yeni-bir-makale-optimal-fractional-fourier-filtering-for-graph-signals","status":"publish","type":"post","link":"https:\/\/umram.bilkent.edu.tr\/index.php\/tr\/2021\/06\/24\/umramdan-yeni-bir-makale-optimal-fractional-fourier-filtering-for-graph-signals\/","title":{"rendered":"UMRAM&#8217;dan Yeni Bir Makale: Optimal Fractional Fourier Filtering for Graph Signals"},"content":{"rendered":"<p><a href=\"https:\/\/umram.bilkent.edu.tr\/index.php\/teams\/aykut-koc\/\">Aykut Ko\u00e7<\/a>&#8216;un grafik sinyal i\u015fleme (GSP) \u00fczerine \u00e7al\u0131\u015fmas\u0131, yak\u0131n zamanda IEEE Transactions on Signal Processing&#8217;de yay\u0131nland\u0131.<\/p>\n<p>Grafik sinyal i\u015flemeye (GSP) bu katk\u0131da, Dr. Ko\u00e7 ve i\u015fbirlik\u00e7ileri, kesirli Fourier alanlar\u0131nda optimal filtreleme problemini grafikler \u00fczerinde form\u00fcle etmekte ve GSP i\u00e7in kapal\u0131 form \u00e7\u00f6z\u00fcm\u00fcn\u00fc sunmaktad\u0131r. Grafiklerdeki optimal Wiener filtreleme problemini kesirli Fourier alanlar\u0131na genelliyoruz. Bu, s\u0131radan Fourier alanlar\u0131nda kar\u015f\u0131l\u0131k gelen klasik problemin genelle\u015ftirilmesidir ve kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm s\u0131ras\u0131n\u0131 se\u00e7medeki ek serbestlik derecesi sayesinde daha d\u00fc\u015f\u00fck hatalar anlam\u0131nda geli\u015fmi\u015f performans sunma potansiyeline sahiptir.<\/p>\n<p>Optimum kesirli Fourier alan\u0131 filtreleme problemi teorik olarak GSP \u00e7er\u00e7evesine genelle\u015ftirildi ve kesirli alanlarda filtrelemenin tepe frekans\u0131 alan\u0131ndaki filtrelemeden daha k\u00fc\u00e7\u00fck hata de\u011ferleri verdi\u011fi birka\u00e7 say\u0131sal uygulama g\u00f6sterildi.<\/p>\n<p>Ne grafik yap\u0131s\u0131nda ne de grafik sinyallerinde herhangi bir k\u0131s\u0131tlay\u0131c\u0131 varsay\u0131mda bulunmad\u0131k. Bu nedenle, \u00f6nerilen kesirli grafik Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc filtreleme \u00e7er\u00e7evesi, \u00e7ok \u00e7e\u015fitli keyfi ko\u015fullar alt\u0131nda uygulanabilir.<\/p>\n<p>Makaleye [<a href=\"https:\/\/ieeexplore.ieee.org\/abstract\/document\/9435933\">buradan<\/a>] ula\u015fabilirsiniz.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u00d6zet:<\/strong><\/p>\n<p>Graph signal processing has recently received considerable attention. Several concepts, tools, and applications in signal processing such as filtering, transforming, and sampling have been extended to graph signal processing. One such extension is the optimal filtering problem. The minimum mean-squared error estimate of an original graph signal can be obtained from its distorted and noisy version. However, the best separation of signal and noise, and thus the least error, is not always achieved in the ordinary Fourier domain, but rather a fractional Fourier domain. In this work, the optimal filtering problem for graph signals is extended to fractional Fourier domains, and theoretical analysis and solution of the proposed problem are provided along with computational cost considerations. Numerical results are presented to illustrate the benefits of filtering in fractional Fourier domains.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aykut Ko\u00e7&#8216;un grafik sinyal i\u015fleme (GSP) \u00fczerine \u00e7al\u0131\u015fmas\u0131, yak\u0131n zamanda IEEE Transactions on Signal Processing&#8217;de yay\u0131nland\u0131. Grafik sinyal i\u015flemeye (GSP) bu katk\u0131da, Dr. Ko\u00e7 ve i\u015fbirlik\u00e7ileri, kesirli Fourier alanlar\u0131nda optimal filtreleme problemini grafikler \u00fczerinde form\u00fcle etmekte ve GSP i\u00e7in kapal\u0131 form \u00e7\u00f6z\u00fcm\u00fcn\u00fc sunmaktad\u0131r. Grafiklerdeki optimal Wiener filtreleme problemini kesirli Fourier alanlar\u0131na genelliyoruz. Bu, s\u0131radan Fourier [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":11683,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[445],"tags":[],"_links":{"self":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/11686"}],"collection":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/comments?post=11686"}],"version-history":[{"count":1,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/11686\/revisions"}],"predecessor-version":[{"id":11687,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/11686\/revisions\/11687"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media\/11683"}],"wp:attachment":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media?parent=11686"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/categories?post=11686"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/tags?post=11686"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}