Image processing with the fractional Fourier transform: synthesis, compression and perspective projections
Author
Yetik, I Şamil
Advisor
Özaktaş, Haldun M.
Date
2000Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Show full item recordAbstract
In this work, first we give a summary of the fractional Fourier transform
including its definition, important properties, generalization to two-dimensions
and its discrete counterpart. After that, we repeat the concept of filtering in
the fractional Fourier domains and give multi-stage and multi-channel filtering
configurations. Due to the nonlinear nature of the problem, the transform
orders in fractional Fourier domain filtering configurations have usually not
been optimized but chosen uniformly up to date. We discuss the optimization
of orders in the multi-channel filtering configuration. In the next part of this
thesis, we discuss the application of fractional Fourier transform based filtering
configurations to image representation and compression. Next, we introduce the
fractional Fourier domain decomposition for continuous signals and systems. In
the last part, we analyse perspective projections in the space-frequency plane
and show that under certain conditions they can be approximately modeled in
terms of the fractional Fourier transform.
Keywords
Fractional Fourier transformsSignal and system synthesis
İmage representation and compression
Perspective projections