Image Processing Method Based On Fractional Fourier Transform And Applied Research

The Fourier Transform (FT) is one of the most important mathematical tools used in information processing, optical image processing and some other areas. The fractional Fourier transform (FrFT) is a generalization of the traditional FT, and has inherited the characteristics of FT. FrFT also has some special features, can be used in some other areas where FT has not been used. And FrFT is a linear transform and continuous in angle, which are very convenient for some applied area. The FrFT is closely connected with the optical imaging system, which is very suitable for digital image processing. And it is a new research area using FrFT for digital image processing.On the basis of study the FrFT theory, its digital computation, and its relationship with optical imaging system, the main aim of this paper is to study the applications of FrFT in blurred image restoration, to research the image edge detection in the fractional Fourier domain. A defocused blurred imaging model based on FrFT is established, which uncover the image blur due to the continuous FrFT process leading to redistribution of magnitude and phase of image. This is a great different from traditional image restoration method. Using this imaging model combing with the clarity-evaluation-function, so the FrFT's order can be changed adaptively. Experimental results show this approach is superior to traditional restoration method and can improve quality of image, which make it more suitable for real-time environment. Then, analysis the theory of image edge detection based on FrFT, constructs an optical detection system for real-time image edge detection, it has developed a new way for image analysis, such as image model recognition and target detection etc.The main contributions of this dissertation are summarized as follows:First, an image restoration method for adaptive defocused image restoration is proposed based on FrFT combing with the image clarity-evaluation-function. Experimental simulation results show the effectiveness of this method, can improve image sharp. It is suitable for real application environment with the optical system. Second, according to the image different parts changing characteristic while the FrFT order is small, an edge detection method based on FrFT is proposed in this paper. Comparing with traditional space arithmetic operator, this approach has some advantages, and can improve the edge of image.