Studies on image encryption compression and watermarking using multiple parameter discrete fractional fourier transform

Abstract

In image processing the transforms plays a vital role in wide range of applications such as image analysis encryption compression and watermarking etc Earlier in image processing, several transforms have been used like Discrete Cosine Transform Discrete Wavelet Transform Fourier Transforms Hotelling Transform etc Among all of them Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components Later it has been recognized that the integral transforms as FT etc are replaced by their respective fractional counter parts as FRFT et. This further enhances an additional degree of freedom incorporated by fractional order parameter In every area where FT and frequency domain concept are used the scope exists for potential generalization and implementation using FRFT and its generalized version newlineWith the advent of computers and enhanced computational capabilities the Discrete Fourier Transform came into existence in evaluation of FT for real time processing Further for efficient implementation of DFT is done with the help of Fast Fourier Transform algorithms To Analyze and compute signal in digital domain the Discrete Fractional Fourier Transform came into the existence with several definitions as adopted by various researchers The DFRFT is a generalization of the discrete Fourier transform with one additional order parameter But if the DFRFT extended to N order parameters where N is the number of the input N data points, this newly derived DFRFT is known as multipleparameter discrete fractional Fourier transform It also shows to have all of the desired properties for fractional transforms The MPDFRFT will be converted to the DFRFT when all of its order parameters are the same newline newline