Research On Image Encryption And Information Processing Techniques Based On Fractional Transform Optics

Optical information processing, which has been developing recently, is a very important part of information science. Whereas, the optical information encryption and image processing is one of the most important research contents of information processing, which has been widely used in various security protection domains, such as country security, personal information protection, wireless transmission, etc., and whose research results can be directly applied to encryption techniques.From recent research progress, we notice that the monochromatic laser light is often used for illumination in optical information processing, and the reconstructed images would lose their color information, therefore we introduce a new optical color image encryption method by wavelength multiplexing and tricolor theory of a color image, combined with several optical fractional transforms and encryption techniques to strengthen information protection. Then, we have studied some image synthesis methods including image fusion and subtraction. As we know, wavelet transform and wavelet packet transform have been widely used to digital image processing and successfully applied in de-noising, data classification, image compression and encryption in wired/wireless communication, such as video, image, music, etc. Combined with fractional Fourier transform, we apply fractional wavelet transform and fractional wavelet packet transform to image encoding. These two methods can not only improve encryption security, but also be used in optical and digital information processing, and we expect that our research results would be well used in digital image encryption and information coding one day.The whole thesis, focused on optical information encoding and image processing, and based on the double random phases encryption method and combined with fractional Fourier optics, has accomplished several works, which are organized as follows:In Chapter 1, a brief introduction to the research progress of optical information protection and processing is given. Research methods and basic theories used in this thesis, including Fourier transform, wavelet transform, fractional wavelet transform and fractional Fourier optics, are emphasized, and some basic algorithms of fast Fourier transform and discrete fractional Fourier transform are also introduced.In Chapter 2, starting from the relationship between the Wigner transformation and the fractional Fourier transform, we apply the fractional Fourier transform to the spatial filtering. In the process of filtering, the noise can be simulated as the chirp functions or their linear combination, which can be filtered at the corresponding fractional planes, and also the actual positions can be exactly obtained. The beam quality can be improved by multi-times fractional filtering. The GUI (Graph User Interface) is established with Matlab in digital processing to realize real-time spatial filtering.In Chapter 3, we briefly introduce the basic theory of double random image encryption menthod proposed by Javidi in 1995 and optical image coding technique based on fractional Fourier transforms. And finally, we also propose a new method for image encryption based on Hartley transform, which is a real transform and whose data calculation can be reduced in the computer simulation. The encoding and decoding processes and the problems that should be noticed in the simulations are introduced in this Chapter. We numerically demonstrate that our algorithm for image encryption with a Hartley transform and a random pure intensity mask is still safe under a bare decryption attack when the random pure intensity is properly chosen. The information can be well protected under both bare decryption and incorrect decryptions.In Chapter 4, the image encryption methods based on fractional wavelet transform and fractional wavelet packet transform are proposed, in which fractional orders, a series of scaling factors and wavelet packet filter are keys in decoding. They combine the virtues of wavelet transform, wavelet packet transform and fractional Fourier transform, and can also realize the partial encryption as wavelet transform encoding. It is much more flexible and effective than wavelet or wavelet packet encryptions. Some possible optical implementations are demonstrated and numerical simulation results are used to prove their possibility. In Chapter 5, a new method is proposed for optical color image encryption by wavelength multiplexing based on lensless Fresnel transform holograms. The image is separated into red, green and blue three channels, and each channel is independently encrypted. The system parameters of Fresnel transforms and random phase masks in each channel are keys in image encryption and decryption. The keys can be added by iteratively employing the Fresnel transforms for several times. Only when all the correct keys are presented, can the original color image be recovered. When keys of only one or two channels are correct, the color information is distorted, and people also cannot obtain the correct information. A pure optical architecture with multichannel implementation and an optoelectronic realization with single channel method are designed in this section, and computer simulations are given to prove the possibility of the proposed idea.In Chapter 6, we propose a new method for color image coding and synthesis based on fractional Fourier transforms and wavelength multiplexing with digital holography. A color image is divided into three channels and each channel, in which the information is encrypted with different wavelength, fractional orders and random phase masks, is independently encrypted or synthesized. The system parameters are additional keys and this method would improve the security of information encryption. The images fused or subtracted by phase shifting technique, is more beautiful and meaningful than the original images. At last, the realization for color image encryption and synthesis is also proposed with some simulation results to show the possibility of the proposed idea.In Chapter 7, we propose a new cryptology in dual fractional Fourier-wavelet domain, which is calculated by discrete fractional Fourier transform and wavelet decomposition. This can be done by dividing an authentic color image into three segments, each of which is encrypted independently with different fractional orders and different wavelengths. Then in each segment, the information is also decomposed into several parts by WT, with each part coded with different random phases. Therefore these keys can be assigned to a group of authorized persons or saved in several places. Only in the case that all these persons present their corresponding portions and synthesize the whole authentic image correctly, can they access the correct information. In the second part of this Chapter, we resolve an optical puzzle in OPN journal with tricolor theory of a color image and the absorption property of light transmission in a certain medium. The Matlab simulation gives corresponding results, which explain that the scene of a color image can be changed by absorbing or transmitting different wavelengths, and that improve the actual application of tricolor theory.While in the last Chapter, we conclude our works and point out some existed problems in our studies, which should be improved in our future work.