Hülya KODAL SEVİNDİR, Cüneyt YAZICI, Süleyman ÇETİNKAYA

Eksik Veri Temininde Shearlet Dönüşümünün Asimptotik Analizi

Asimptotik analiz bir algoritmanın performansı hakkında bize yol gösterir. Matematiksel ispatlarla yapılmış bir asimptotik analiz, algoritmaların performansını anlamlandırmada oldukça güçlü bir yöntemdir. Shearlet dönüşümü ise dalgacık dönüşümünün etkili bir geliştirmesi olarak son yıllarda ortaya çıkmış matematiksel bir yöntemdir. Bu amaçla bu makalede, görüntülerdeki olası kayıp verinin yeniden temini açısından shearlet dönüşümü, dalgacık dönüşümü ile asimptotik olarak kıyaslanmıştır. Görüntü işleme uygulamaları içerisinde, görüntüler üzerinde eksik (kayıp) olan verinin yeniden elde edilmesi amacıyla, eksik verinin şeklen yatay konumlanmış dikdörtgen şeklinde olması durumunda Shearlet dönüşümü için asimptotik analizi yapılmıştır.

Anahtar Kelimeler:

Shearlet Dönüşümü, Dalgacık Dönüşümü, Eksik Verinin Elde Edilmesi, Asimptotik Analiz

Asymptotic Analysis of Shearlet Transfom for Inpainting

Supply of missing data, also known as inpainting, is an important application of image processing.Wavelets are commonly used for inpainting algorithms. Shearlet transform which is an affinetransformation is the improvement of the wavelet transform. An asymptotic analysis may help to evaluatethe performance of an algorithm. In this article we compare the asymptotical analysis for wavelet andshearlet transforms in the case of inpainting where the missing data is shaped like a rectangle.

Keywords:

Shearlet Transform, Wavelet Transform, Inpainting, Asymptotic Analysis,

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