Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics

There are many image processing applications which require more sophisticated computational techniques. Among these applications are image encryption, image wa- termarking, and many others. In this thesis, di erent computational techniques based on fractional Fourier transform, discrete orthogonal polynomials, chaotic systems and reversible logical gates are studied, analysed and proposed to be applied with the aforementioned applications. However, the range of applicability can be extended to other application domains.The purpose of image encryption and image watermarking is to hide the image information, except for legitimate users and authenticate the visual content, respec- tively. In order to achieve this purpose, a detailed study has been carried out to propose novel image transforms based on the theory of fractional Fourier transform and discrete orthogonal polynomials.These transforms are applied with the theory of chaotic systems and reversible logical gates to enhance the performance of the afore- mentioned applications. While the image transforms are used to map an image from the spatial domain into the frequency domain, the chaotic dynamical systems and reversible logical gates are used to randomize image pixels to ensure the security of these applications

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