The Applications And Researches Of Fractional Fourier Transform In Digital Image Processing

Introducing FRFT into digital image processing field is a new direction of image technology development. The FRFT is closely connected with optical system and can describe all diffraction process of optical imaging system. Therefore, it is very suitable for digital image processing.According to mathematic and optical charactertics of FRFT and internal relations between FRFT and digital image, we have proposed several digital image processing arithmetic based on FRFT domain, which are used to two directions: image restoring and digital image security. The researches mainly include the following three aspects.Considering the mutual connects between FRFT and optical diffraction process, a defocused imaging model based on FRFT is established to explain the blur phenomenon of defocusing image on the basis of the internal connections of FRFT and optical diffract imaging system. The defocused imaging model is greatly different from the traditional PSF model, which enables to uncover the blur nature of non-focus image: the continuous FRFT process lead to redistributions of magnitude and phase of image. An image restoration approaches using the novel model are given to handle the blurred defocused image, which can make the image sharp and improve quality of image. The experiments demonstrate that FRFT restoring method is superior to the convenient PSF restoring method.In the field of digital copyright protection, we adopted the current popular CDMA technology to our digital watermark system and purposed a CDMA spread spectrum digital watermark schema based on FRFT domain. The watermarking image is divided into many segments. By utilizing different orthogonal Gold codes, every segment of watermarking image is independently modulated into the CDMA watermarking data which is embedded the low frequency magnitude coefficients of FRFT of host image. The CDMA technique not only can enhance the robustness of watermark but also can compress the data of the modulated watermark for increasing data hiding capacity. Moreover, the FRFT domain watermarking system has the property of spatial-domain and frequency-domain watermarking system.In digital image encrypting protection system, a new method based on the variety of the FRFT and pseudo- randomness, complexity of chaotic sequences for encrypting image using encoding both space domain and FRFT domain is proposed, which can improve system security. Finally, we have studied double-random phase encrypting method in FRFT domain for the optical image security system.In additional to image restoration and image security protection, the FRFT are also applied to other digital image processing fields such as pattern recognization, brim detection. With the development of FRFT theory and technology, the application in digital image processing will be more wide and deep.