{"id":1016,"date":"2023-03-22T13:24:29","date_gmt":"2023-03-22T10:24:29","guid":{"rendered":"https:\/\/legendhomework.com\/tr\/?p=1016"},"modified":"2023-03-22T13:24:29","modified_gmt":"2023-03-22T10:24:29","slug":"ses-sinyallerinin-ayrilmasi-multimedya-bolumu-multimedya-bolumu-odevleri-multimedya-bolumu-tez-yaptirma-multimedya-bolumu-odev-ucretleri","status":"publish","type":"post","link":"https:\/\/legendhomework.com\/tr\/ses-sinyallerinin-ayrilmasi-multimedya-bolumu-multimedya-bolumu-odevleri-multimedya-bolumu-tez-yaptirma-multimedya-bolumu-odev-ucretleri\/","title":{"rendered":"Ses Sinyallerinin Ayr\u0131lmas\u0131 \u2013 Multimedya B\u00f6l\u00fcm\u00fc \u2013 Multimedya B\u00f6l\u00fcm\u00fc \u00d6devleri \u2013 Multimedya B\u00f6l\u00fcm\u00fc Tez Yapt\u0131rma \u2013Multimedya B\u00f6l\u00fcm\u00fc \u00d6dev \u00dccretleri"},"content":{"rendered":"

Olas\u0131l\u0131k<\/span><\/strong><\/h3>\n

Algoritman\u0131n en b\u00fcy\u00fck avantaj\u0131 yinelemesiz do\u011fas\u0131d\u0131r; ancak, olas\u0131l\u0131\u011f\u0131n en aza indirilmesi do\u011frudan garanti edilmez. Yine de olas\u0131l\u0131k, modellemenin do\u011fas\u0131n\u0131 anlamak i\u00e7in uygun bir ara\u00e7t\u0131r. Bir \u03c4 (T = 1) konu\u015fland\u0131rmak, kaynak ba\u015f\u0131na bir parametre kullanarak (7.8)’deki p(S|\u03c8) kaynak da\u011f\u0131l\u0131m\u0131n\u0131 parametrele\u015ftirmeyle tutarl\u0131d\u0131r. Daha fazla \u03c4 konu\u015fland\u0131r\u0131ld\u0131k\u00e7a, olas\u0131l\u0131\u011f\u0131n daha esnek bir parametrele\u015ftirmesi uygulan\u0131r.<\/span><\/p>\n

Olas\u0131l\u0131k, Fourier teknikleri kullan\u0131larak basit bir \u015fekilde hesaplanabilir. Bu ayn\u0131 zamanda do\u011frulama\/genelle\u015ftirme hatas\u0131n\u0131n hesaplanmas\u0131n\u0131 ve sonu\u00e7 olarak minimum genelleme hatas\u0131 elde etmeyi ama\u00e7layan optimal t’leri se\u00e7menin ilkeli bir yolunu sa\u011flar. Ancak, bu tart\u0131\u015fma bu b\u00f6l\u00fcm\u00fcn kapsam\u0131 d\u0131\u015f\u0131ndad\u0131r.<\/span><\/p>\n

Ses Sinyallerinin Ayr\u0131lmas\u0131<\/span><\/strong><\/h3>\n

Bu \u00f6rnekte ama\u00e7, ICA’n\u0131n ses sinyallerinin ayr\u0131lmas\u0131na nas\u0131l uyguland\u0131\u011f\u0131n\u0131 g\u00f6stermektir. Bu, g\u00f6sterilen kokteyl partisi problemi ile ba\u011flant\u0131l\u0131 olarak k\u00f6r sinyal ayr\u0131m\u0131n\u0131n \u00f6zel bir durumu olarak d\u00fc\u015f\u00fcn\u00fclebilir.<\/span><\/p>\n

Mevcut \u00f6rnek, istatistiksel olarak ba\u011f\u0131ms\u0131z oldu\u011fu varsay\u0131lan \u00fc\u00e7 ki\u015finin konu\u015fmas\u0131yla ilgilidir. Sinyallerin \u00f6rnekleme frekans\u0131 11.025 Hz’dir ve her biri 50.000 \u00f6rnekten olu\u015fur. Bilinen sabit bir 3×3 kar\u0131\u015ft\u0131rma matrisi ile do\u011frusal bir anl\u0131k kar\u0131\u015ft\u0131rma devreye al\u0131n\u0131r ve ICA ayr\u0131m\u0131n\u0131n nicel bir de\u011ferlendirmesini sa\u011flar.<\/span><\/p>\n

Kaynak ve kar\u0131\u015ft\u0131rma sinyalleri g\u00f6sterilir. Genel olarak bu varsay\u0131mlar, yank\u0131, g\u00fcr\u00fclt\u00fc, gecikme ve \u00e7e\u015fitli do\u011frusal olmayan etkiler nedeniyle ger\u00e7ek d\u00fcnya uygulamalar\u0131nda ge\u00e7erli olmayacakt\u0131r. Bu gibi durumlarda, a\u00e7\u0131kland\u0131\u011f\u0131 gibi, daha ayr\u0131nt\u0131l\u0131 kaynak ayr\u0131m\u0131 gerekir. Ay\u0131rma i\u015fleminin sonu\u00e7lar\u0131n\u0131 de\u011ferlendirmek i\u00e7in, tan\u0131mlanm\u0131\u015f s\u00f6zde sistem matrisini dikkate al\u0131yoruz.<\/span><\/p>\n

A’n\u0131n tahmin edilen kar\u0131\u015ft\u0131rma matrisi oldu\u011fu yerde, P bir perm\u00fctasyon matrisidir ve Cs(0) tahmin edilen kaynak sinyallerinin \u00e7apraz korelasyon matrisidir. Ay\u0131rma ba\u015far\u0131l\u0131 olursa, sistem matrisi birim matrise e\u015fittir.<\/span><\/p>\n

PCA Kullanarak Ses Ay\u0131rma<\/span><\/strong><\/h3>\n

A\u00e7\u0131klanan PCA, basit ve nispeten h\u0131zl\u0131 oldu\u011fu i\u00e7in s\u0131kl\u0131kla kullan\u0131l\u0131r. Ayr\u0131ca kaynaklar\u0131 g\u00fcce (varyansa) g\u00f6re s\u0131ralayarak kaynak say\u0131s\u0131n\u0131 azaltma imkan\u0131 sunar. PCA ayr\u0131m\u0131n\u0131n sonucu ve kar\u015f\u0131l\u0131k gelen sistem matrisi g\u00f6sterilir. A\u00e7\u0131k\u00e7as\u0131, tahmini kaynaklar orijinal kaynaklarla kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda sonu\u00e7 zay\u0131ft\u0131r. Bu, sistem matrisinin incelenmesiyle de do\u011frulan\u0131r.<\/span><\/p>\n

Molgedey\u2013Schuster ICA Kullanarak Ses Ay\u0131rma<\/span><\/strong><\/p>\n

Molgedey-Schuster ICA algoritmas\u0131n\u0131n ana avantaj\u0131, yinelemesiz olmas\u0131 ve dolay\u0131s\u0131yla \u00e7ok h\u0131zl\u0131 olmas\u0131d\u0131r. Standart bir T = 1 ICA kullan\u0131ld\u0131 ve \u03c4 = 1 se\u00e7imi en iyi performans\u0131 verdi.<\/span><\/p>\n

Tahmini ses sinyallerinde ay\u0131rma g\u00f6sterilmektedir. Orijinal kaynak sinyalleriyle kar\u015f\u0131la\u015ft\u0131rma, \u00e7ok iyi bir ayr\u0131m oldu\u011funu g\u00f6sterir. Sistem matrisi ve ek bir dinleme testi de bu sonucu do\u011frulamaktad\u0131r.<\/span><\/p>\n

\u00c7ok yayg\u0131n olarak kullan\u0131lan Bell-Sejnowski ICA [6], s\u0131f\u0131r g\u00fcr\u00fclt\u00fc durumunda sunulanlar gibi varsay\u0131mlarla maksimum olas\u0131l\u0131\u011fa e\u015fde\u011ferdir. Bell\u2013Sejnowski ICA, olas\u0131l\u0131\u011f\u0131n do\u011fal gradyan\u0131 ile orant\u0131l\u0131 olarak g\u00fcncelleyerek kar\u0131\u015f\u0131m matrisinin bir tahminini yinelemeli olarak hesaplar.<\/span><\/p>\n

Ad\u0131m boyutu (gradyan parametresi) ba\u015flang\u0131\u00e7ta 10\u22124 idi ve ikiye b\u00f6lme kullan\u0131larak bir \u00e7izgi aramas\u0131 kullan\u0131ld\u0131. Algoritma, negatif log-olas\u0131l\u0131k 10\u221212’nin alt\u0131nda oldu\u011funda sonland\u0131r\u0131ld\u0131. Yinelemeli do\u011fas\u0131 nedeniyle, bu algoritma Molgedey-Schuster algoritmas\u0131ndan \u00e7ok daha fazla zaman al\u0131r.<\/span><\/p>\n

Ayr\u0131l\u0131\u011f\u0131n sonu\u00e7lar\u0131 g\u00f6sterilir. A\u00e7\u0131k\u00e7as\u0131, sistem matrisi, artan hesaplama y\u00fck\u00fc pahas\u0131na birim matrise oldu\u011fundan daha yak\u0131nd\u0131r.<\/span><\/p>\n

Sistem matrisinin birim matristen sapma normunu ve hesaplama s\u00fcresini listeler. A\u00e7\u0131k\u00e7as\u0131, PCA, \u00e7ok s\u0131n\u0131rl\u0131 ay\u0131rma yetenekleri nedeniyle her iki ICA algoritmas\u0131 taraf\u0131ndan daha iyi performans g\u00f6sterdi. Her iki ICA algoritmas\u0131 da \u00e7ok iyi performans g\u00f6sterdi.<\/span><\/p>\n

En b\u00fcy\u00fck fark, hesaplama s\u00fcresidir; MS-ICA, BS-ICA’dan 200 kat daha h\u0131zl\u0131yd\u0131. BS-ICA algoritmas\u0131n\u0131n avantaj\u0131, yeterli hesaplama s\u00fcresi sa\u011fland\u0131\u011f\u0131nda sistem matrisinin birli\u011fe \u00f6nemli \u00f6l\u00e7\u00fcde daha yak\u0131n olabilmesidir.<\/span><\/p>\n

BS-ICA’y\u0131 ba\u015flatmak i\u00e7in MS-ICA’n\u0131n kullan\u0131ld\u0131\u011f\u0131 bir MS-ICA ve BS-ICA melezi bariz g\u00f6r\u00fcnmektedir. Ayr\u0131lm\u0131\u015f sinyalleri dinleyerek, ICA sonu\u00e7lar\u0131 aras\u0131ndaki fark\u0131 s\u00f6ylemek neredeyse imkans\u0131zd\u0131.<\/span><\/p>\n

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Ses dalga<\/a> boyu<\/span>
\n1 oktav ses<\/span>
\nOktav ses aral\u0131\u011f\u0131<\/span>
\nKedi Kovucu ses frekans\u0131<\/span>
\n4 oktav ses<\/span>
\nHayvanlar\u0131n ses duyma frekanslar\u0131<\/span>
\nKibariye sesi ka\u00e7 oktav<\/span>
\nK\u00f6pekler hangi sesleri duyar<\/span><\/p>\n

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G\u00f6r\u00fcnt\u00fc Kar\u0131\u015f\u0131mlar\u0131n\u0131n Ayr\u0131lmas\u0131<\/span><\/strong><\/h3>\n

ICA’n\u0131n g\u00f6r\u00fcnt\u00fclere uygulanmas\u0131, y\u00fcz tan\u0131madan beyindeki aktif b\u00f6lgelerin lokalizasyonuna kadar bir dizi uygulamada ger\u00e7ekle\u015ftirilmi\u015ftir.<\/span><\/p>\n

Bu b\u00f6l\u00fcmde, g\u00f6r\u00fcnt\u00fc b\u00f6l\u00fcmleme i\u00e7in PCA’n\u0131n aksine veya PCA ile kombinasyon halinde ICA kullanan baz\u0131 temel \u00f6zellikleri g\u00f6steriyoruz. Ama\u00e7, bir dizi g\u00f6r\u00fcnt\u00fcden, ortak \u00f6zelliklerin farkl\u0131 g\u00f6r\u00fcnt\u00fclere ayr\u0131ld\u0131\u011f\u0131 s\u0131ral\u0131 g\u00f6r\u00fcnt\u00fcleri \u00e7\u0131karmakt\u0131r.<\/span><\/p>\n

Mevcut durumda ICA, ham g\u00f6r\u00fcnt\u00fclere dayanmaktad\u0131r; ancak, ilke olarak, b\u00f6l\u00fctleme, g\u00f6r\u00fcnt\u00fclerden \u00e7\u0131kar\u0131lan \u00f6zelliklerden de yap\u0131labilir. Bu \u00f6rnekte g\u00f6sterilen basit veri k\u00fcmesi kullan\u0131lm\u0131\u015ft\u0131r.<\/span><\/p>\n

Her sat\u0131r\u0131n bir g\u00f6r\u00fcnt\u00fcy\u00fc temsil etmesi i\u00e7in P \u00d7 N kaynak matrisi S’de yeniden d\u00fczenlenen N = 9100 (91’e 100) piksellik P = 4 orijinal kaynak g\u00f6r\u00fcnt\u00fc vard\u0131r. M = 6 ile M \u00d7 N sinyal matrisi X, a\u015fa\u011f\u0131daki M \u00d7 P kar\u0131\u015ft\u0131rma matrisi kullan\u0131larak \u00fcretilir.<\/span><\/p>\n

PCA Kullanarak G\u00f6r\u00fcnt\u00fc B\u00f6l\u00fcmleme<\/span><\/strong><\/h3>\n

Y\u00fcz veri k\u00fcmesine PCA uygulamas\u0131n\u0131n sonucu g\u00f6sterilir. S\u0131f\u0131r olmayan \u00f6zde\u011ferlerin say\u0131s\u0131 do\u011fru olarak 4 olarak belirlenmi\u015ftir. Ka\u015f ve a\u011f\u0131z konumlar\u0131n\u0131n \u00e7iftler halinde \u00e7al\u0131\u015ft\u0131\u011f\u0131na dikkat edin; a\u011f\u0131z “g\u00fcl\u00fcmsedi\u011finde” “\u00fczg\u00fcn” olamaz ve ayn\u0131 \u015fey ka\u015flar i\u00e7in de ge\u00e7erlidir.<\/span><\/p>\n

PCA bu davran\u0131\u015f\u0131 alg\u0131layabilir ancak 2. ve 3. kaynaklarda hem ka\u015flar\u0131 hem de a\u011f\u0131z par\u00e7alar\u0131n\u0131 kar\u0131\u015ft\u0131r\u0131r. Ayr\u0131ca, 1. kaynakta yaln\u0131zca burun bulunur. veriler i\u00e7in her zaman uygun olmayan varyanst\u0131r.<\/span><\/p>\n

Molgedey\u2013Schuster ICA kullanarak G\u00f6r\u00fcnt\u00fc B\u00f6l\u00fcmleme<\/span><\/strong><\/p>\n

G\u00f6r\u00fcnt\u00fcler \u00fczerinde ICA, X sinyal matrisine veya devrik X\u22a4’ye uygulanabilir. \u0130lk durumda N = piksel say\u0131s\u0131 ve M = kaynaklardaki piksellerin ba\u011f\u0131ms\u0131z oldu\u011fu varsay\u0131m\u0131na kar\u015f\u0131l\u0131k gelen dizideki g\u00f6r\u00fcnt\u00fc say\u0131s\u0131.<\/span><\/p>\n

Bu durumda kaynaklar g\u00f6r\u00fcnt\u00fclerdir ve kar\u0131\u015ft\u0131rma matrisi zaman dizisidir. \u0130kinci durumda, N = s\u0131radaki g\u00f6r\u00fcnt\u00fc say\u0131s\u0131 ve M = ba\u011f\u0131ms\u0131z s\u00fcr\u00fc\u015f zaman dizisi kaynaklar\u0131na kar\u015f\u0131l\u0131k gelen piksel say\u0131s\u0131. B\u00f6ylece, kar\u0131\u015ft\u0131rma matrisi (eigen)g\u00f6r\u00fcnt\u00fclere kar\u015f\u0131l\u0131k gelir.<\/span><\/p>\n

Piksel ba\u011f\u0131ms\u0131zl\u0131\u011f\u0131 varsay\u0131ld\u0131\u011f\u0131nda (yani, sinyal matrisi olarak X kullan\u0131ld\u0131\u011f\u0131nda) sonu\u00e7 g\u00f6sterilir. Zamandan ba\u011f\u0131ms\u0131z oldu\u011fu varsay\u0131ld\u0131\u011f\u0131nda (yani, sinyal matrisi olarak X\u22a4 kullan\u0131ld\u0131\u011f\u0131nda) sonu\u00e7 g\u00f6sterilmektedir.<\/span><\/p>\n

Ger\u00e7ek g\u00f6r\u00fcnt\u00fc uygulamalar\u0131 genellikle PCA yerine ICA’y\u0131 tercih eder. Bunun ba\u015fl\u0131ca nedeni, ICA’n\u0131n ortogonal olmayan bir temel \u00fcretebilmesi ve PCA’n\u0131n do\u011fas\u0131nda var olan varyans s\u0131ralamas\u0131 taraf\u0131ndan k\u0131s\u0131tlanmamas\u0131d\u0131r.<\/span><\/p>\n

Kaynak say\u0131s\u0131n\u0131 belirlemek i\u00e7in ICA’ya \u00f6n i\u015fleme olarak PCA’n\u0131n kullan\u0131lmas\u0131 ba\u015far\u0131l\u0131 olmu\u015ftur. Ayr\u0131ca, kar\u0131\u015ft\u0131rma matrisinin PCA tahmini, algoritma gibi yinelemeli bir ICA \u015femas\u0131 i\u00e7in ba\u015flatma olarak kullan\u0131labilir.<\/span><\/p>\n

Molgedey-Schuster algoritmas\u0131n\u0131 kullanarak ICA ger\u00e7ekle\u015ftirmek, kar\u015f\u0131la\u015ft\u0131r\u0131labilir hesaplama maliyetinde PCA’dan daha iyi sonu\u00e7lar verir.<\/span><\/p>\n

Piksel ba\u011f\u0131ms\u0131zl\u0131\u011f\u0131na kar\u015f\u0131 zamandan ba\u011f\u0131ms\u0131z se\u00e7im, eldeki sorunla ilgilidir. Yukar\u0131daki g\u00f6r\u00fcnt\u00fc b\u00f6l\u00fctleme probleminde, piksel ba\u011f\u0131ms\u0131zl\u0131\u011f\u0131 en iyi sonucu verdi; ancak, di\u011fer durumlar zamandan ba\u011f\u0131ms\u0131z olmay\u0131 tercih etmi\u015ftir.<\/span><\/p>\n

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