分数傅里叶变换在数字图像处理中的应用研究
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摘要
将分数傅里叶变换(FRFT,Fractional Fourier Transform)用于数字图像处理领域中是图像技术发展的一个新方向。由于FRFT与光学成像有着内在的联系,可用它来描述光学成像衍射过程,因而它非常适合于数字图像处理。
本文在分析了FRFT的数学、光学特性和FRFT与数字图像关系基础上,提出了基于FRFT变换域的数字图像处理算法。这些算法主要集中于图像复原和数字图像信息安全两个方向,内容包括以下三个方面:
首先依据FRFT与光学衍射成像系统的内在联系,利用FRFT分析和解释了光学成像过程中的散焦模糊现象,进而构建FRFT散焦成像模型。FRFT散焦成像模型完全不同于传统的点传播模型PSF,它揭示了光学成像系统中散焦图像的模糊本质是在于连续FRFT过程导致图像的幅度、相位发生改变。由此本文提出了基于FRFT散焦成像模型图像复原算法,它可以提高散焦模糊图像的清晰度、改善图像质量,解决了数字图像中散焦模糊问题。最后将FRFT散焦图像复原方法与传统PSF模型散焦复原方法进行对比实验,结果显示FRFT散焦复原法的恢复效果优于传统方法。
在数字版权安全保护中,依据FRFT的光学衍射成像系统的内在联系,本文并将当前流行的CDMA扩频通信技术原理融入到水印系统中,由此提出了基于CDMA扩频的FRFT域数字图像水印实现算法。将水印数据分解成一些片断,每个片断代表不同的CDMA用户数据,每个片断数据用不同的正交Gold码调制成CDMA扩频水印数据,而后将这些CDMA水印数据嵌入到图像的FRFT域的低频系数中。FRFT图像水印同时具有空域水印系统和频域水印系统的特性,CDMA技术能改善水印系统的鲁棒性和安全性、增加水印信息容量。
在数字图像加密保护中,利用FRFT的多样性和混沌序列的复杂性、伪随机性和对初值敏感性,本文提出基于FRFT域和空域混沌序列的双重图像加密算法,它能显著提高加密图像的抗攻击性。另外本文研究了基于非对称FRFT域的双重随机相位图像加解密实现过程。
除了在图像复原与图像安全保护中应用外,FRFT也可应用于数字图像处理领域的其它方向如模式识别、图像边缘检测等。随着FRFT理论技术的发展,FRFT在数字图像处理的应用会更加深入广泛。
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.
本文在分析了FRFT的数学、光学特性和FRFT与数字图像关系基础上,提出了基于FRFT变换域的数字图像处理算法。这些算法主要集中于图像复原和数字图像信息安全两个方向,内容包括以下三个方面:
首先依据FRFT与光学衍射成像系统的内在联系,利用FRFT分析和解释了光学成像过程中的散焦模糊现象,进而构建FRFT散焦成像模型。FRFT散焦成像模型完全不同于传统的点传播模型PSF,它揭示了光学成像系统中散焦图像的模糊本质是在于连续FRFT过程导致图像的幅度、相位发生改变。由此本文提出了基于FRFT散焦成像模型图像复原算法,它可以提高散焦模糊图像的清晰度、改善图像质量,解决了数字图像中散焦模糊问题。最后将FRFT散焦图像复原方法与传统PSF模型散焦复原方法进行对比实验,结果显示FRFT散焦复原法的恢复效果优于传统方法。
在数字版权安全保护中,依据FRFT的光学衍射成像系统的内在联系,本文并将当前流行的CDMA扩频通信技术原理融入到水印系统中,由此提出了基于CDMA扩频的FRFT域数字图像水印实现算法。将水印数据分解成一些片断,每个片断代表不同的CDMA用户数据,每个片断数据用不同的正交Gold码调制成CDMA扩频水印数据,而后将这些CDMA水印数据嵌入到图像的FRFT域的低频系数中。FRFT图像水印同时具有空域水印系统和频域水印系统的特性,CDMA技术能改善水印系统的鲁棒性和安全性、增加水印信息容量。
在数字图像加密保护中,利用FRFT的多样性和混沌序列的复杂性、伪随机性和对初值敏感性,本文提出基于FRFT域和空域混沌序列的双重图像加密算法,它能显著提高加密图像的抗攻击性。另外本文研究了基于非对称FRFT域的双重随机相位图像加解密实现过程。
除了在图像复原与图像安全保护中应用外,FRFT也可应用于数字图像处理领域的其它方向如模式识别、图像边缘检测等。随着FRFT理论技术的发展,FRFT在数字图像处理的应用会更加深入广泛。
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.
引文
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