Weighted Unitary Transforms And Its Applications To Optical Imgae Encryption

Optical information security, which is a branch of the information processing, be-comes a new research topic of the information science. The main methods are imple-mented by the optical transforms, such as the fractional Fourier transform, with the ran-dom key generation algorithms. The fractional Fourier transforms are new analysis meth-ods due to its extensive applications in the areas of optics information security, signalprocessing, pattern recognition and image processing and are applied to the optical imageencryption successfully. However it is showed in this dissertation that the image encryp-tion methods based on the fractional Fourier transform have the common drawbacks insecurity. Therefore searching the more secure and effective image encryption methodsare of great theoretical and practical application values.In this dissertation, weighted unitary transforms are presented. The novel presentedweighted unitary transforms include the fractional Fourier transforms because they be-come fractional Fourier transforms when their vector parameters are chosen the specialdomain. When weighted unitary transforms are applied to the optical image encryption,they can overcome the drawbacks of the optical image encryption based on fractionalFourier transform without increasing the complexity and the optical hardware. The dis-crete weighted unitary transforms are proposed and applied to the optical image encryp-tion. Simulations are presented to verify the security and reliability of the proposed meth-ods. The research work has been summarized as follows:Propose the definition of weighted unitary transforms. The novel weightedcoefficient dependent on the many real free parameters are derived. The transforms de-fined by this weighted coefficient are called the weighted unitary transforms. The newtransforms include the many kinds of fractional Fourier transforms. The weighted uni-tary transforms include all kinds of fractional Fourier transforms. The weighted unitarytransforms correspond to the different kind of fractional Fourier transform when the freeparameters of weighted fractional unitary transforms are elected different domain. Threeweighted unitary transforms are classified according to the different weighted coefficients.Discover the phenomenon that many deciphering keys correspond to a givenencoding key in traditional image encryption methods based on the fractional Fourier transform. The security of the encryption method based on the multi-parameterfractional Fourier transform in the current article are analyzed in detail. Some hiddentroubles are found in the optical image encryption method. The reasons generating thephenomenon are analyzed in the theory. They are the first kind of drawback—- resultedfrom the periodicity of the order parameter; the second kind of drawback—- resultedfrom the arbitrary selection of the order in the real; the third kind of drawback—- resultedfrom the redundant of the vector parameter; the fourth kind of drawback—- resulted fromthe shift of the vector parameter. The simulations verify the conclusion of the theoreticalanalysis.Propose four kinds of the optical image encryption methods based on theweighted unitary transforms. Without increasing computation cost and the complexityof the optical hardware, the image encryption based on the weighted unitary transformsnot only have all the advantages as the weighted fractional Fourier transform have, butalso overcome all the drawbacks resulting from the image encryption methods based onthe fractional Fourier transforms. The image encryption method based on the weightedunitary transforms enhance security and validity of the optical image encryption methods.The optical image encryption methods based on weighted unitary transform-I is proposed,which overcomes the second and third kinds of drawbacks. The optical image encryptionmethods based on the weighted unitary transform-II is proposed, which overcomes the up-per three kinds drawbacks. The optical image encryption methods based on the weightedunitary transform-III is proposed, which overcomes all four kinds of drawbacks. Thedouble blind image encryption method based on the weighted unitary transform-III isproposed on the basis of the upper optical image encryption methods.Propose the algorithm of the discrete weighted unitary transforms and applyit on the image encryption. One kind of discrete algorithm of weighted unitary trans-forms is proposed and applied to the image encryption. An example of a kind of discreteweighted unitary transform is given. It is discrete fractional Fourier transform based onthe analytic eigenvector of the matrix of discrete Fourier transform. When the noveldiscrete fractional Fourier transform is applied to the image encryption, it has better ef-fective than the methods in the present. The security of the image encryption enhancefor the different selection of the analytic basis of fractional Fourier transform. Some dis-crete fractional Fourier transforms are analyzed in detail and demonstrated the reasons that some discrete fractional Fourier transforms have the low precision on some specialorder. The discrete fractional Fourier transforms are classified and proposed the precisionof the discrete fractional Fourier transforms. We summarize the properties of the discretefractional Fourier transforms which has strong convergence to the continuous fractionalFourier transforms.The proposed weighted unitary transform promote the developing of the theory oftransforms. It provides a new effective tool of the optical information processing andadvance the developing of the theory of optical information security.