基于四元数理论的彩色图像信息隐藏技术
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摘要
本论文主要研究了基于四元数理论的彩色图像信息隐藏技术,包括彩色图像的加密、隐写术和数字水印技术。将一幅彩色图像表示为一四元数矩阵,将此矩阵在傅里叶变换前后各乘以一个四元数随机相位掩模函数,以实现彩色图像的加密;将彩色宿主图像表示为一四元数矩阵并进行整体的傅里叶变换或余弦变换,适当修改变换域的系数,从而可以在宿主图像的变换域中嵌入秘密信息或水印图像,以实现信息的隐藏。
本文具体内容包括以下几个方面:
1、应用光学图像加密的思想,将离散四元数傅里叶变换(DOFT)与双随机相位加密技术相结合,把彩色图像作为一个整体进行加密。把待加密彩色图像表示为一离散四元数矩阵,将此四元数矩阵在傅里叶变换前后均进行基于光学原理的双随机相位加密,即在空间域和频率域各乘以一个四元数随机相位掩模函数,实现对彩色图像的加密。由于双随机相位加密技术有很高的安全性,在不知密钥的情况下要解密图像几乎是不可能的,由此保证了加密系统的安全性。文中给出了模拟实验结果,并讨论了高斯噪声和椒盐噪声对实验结果的影响。
2、分析了离散四元数傅里叶变换(DQFT)的特性,并将结论应用到彩色图像的隐写术中。对彩色宿主图像做离散四元数傅里叶变换,利用DOFT的特性,将加密后的图像作为秘密信息隐藏在彩色宿主图像的频率域中,实现秘密信息的隐写。该方法将信息加密与信息隐藏相结合,提高了秘密信息的安全性。
3、分析了离散四元数余弦变换(DQCT)的特性,将离散四元数余弦变换(DQCT)应用于彩色图像的数字水印技术中,提出了一种在彩色图像中嵌入水印的新技术。把彩色宿主图像表示为一四元数矩阵,并进行DOCT变换,利用DQCT的特性,通过修改频率域系数实现彩色水印图像的嵌入。该方法具有较好的抗压缩能力,对高斯噪声、椒盐噪声和图像缩放处理具有较好的鲁棒性。
In this dissertation, color image information hiding technology include color image encryption、steganography and color image watermarking using quaternion is proposed. The color image can be described as a quaternion matrix, by which color images can be processed as a whole, rather than as separated color components in three channels.
The emphases in this thesis are summarized as following:
1、A new method for color-image encryption using Discrete Quaternion Fourier Transforms (DQFT) combined with doubled random-phase encryption as used in the optical implementation is proposed, by which color images can be processed as a whole, rather than as separated color components in three channels, so that the complexity of the encryption system can be effectively reduced without any reduction of its security. The principle of both encryption and decryption is detailed and the robustness of the system has been examined experimentally.
2、A new method for color image steganography using Discrete Quaternion Fourier Transforms(DQFT) is proposed. The host color image should be transformed to the DQFT domain, and the secret image should be encrypted first and then the encrypted color image can be embedded into the DQFT domain of the host image.
3、A new method for color image watermarking using Discrete Quaternion Cosine Transforms (DQCT) is proposed. The watermark image can be embedded in the DQCT domain of the host color image. Experimental results show that this method has good resistance to JPEG compression and is robust against Gaussian noise、salt & pepper noise and image scaling attack.
本文具体内容包括以下几个方面:
1、应用光学图像加密的思想,将离散四元数傅里叶变换(DOFT)与双随机相位加密技术相结合,把彩色图像作为一个整体进行加密。把待加密彩色图像表示为一离散四元数矩阵,将此四元数矩阵在傅里叶变换前后均进行基于光学原理的双随机相位加密,即在空间域和频率域各乘以一个四元数随机相位掩模函数,实现对彩色图像的加密。由于双随机相位加密技术有很高的安全性,在不知密钥的情况下要解密图像几乎是不可能的,由此保证了加密系统的安全性。文中给出了模拟实验结果,并讨论了高斯噪声和椒盐噪声对实验结果的影响。
2、分析了离散四元数傅里叶变换(DQFT)的特性,并将结论应用到彩色图像的隐写术中。对彩色宿主图像做离散四元数傅里叶变换,利用DOFT的特性,将加密后的图像作为秘密信息隐藏在彩色宿主图像的频率域中,实现秘密信息的隐写。该方法将信息加密与信息隐藏相结合,提高了秘密信息的安全性。
3、分析了离散四元数余弦变换(DQCT)的特性,将离散四元数余弦变换(DQCT)应用于彩色图像的数字水印技术中,提出了一种在彩色图像中嵌入水印的新技术。把彩色宿主图像表示为一四元数矩阵,并进行DOCT变换,利用DQCT的特性,通过修改频率域系数实现彩色水印图像的嵌入。该方法具有较好的抗压缩能力,对高斯噪声、椒盐噪声和图像缩放处理具有较好的鲁棒性。
In this dissertation, color image information hiding technology include color image encryption、steganography and color image watermarking using quaternion is proposed. The color image can be described as a quaternion matrix, by which color images can be processed as a whole, rather than as separated color components in three channels.
The emphases in this thesis are summarized as following:
1、A new method for color-image encryption using Discrete Quaternion Fourier Transforms (DQFT) combined with doubled random-phase encryption as used in the optical implementation is proposed, by which color images can be processed as a whole, rather than as separated color components in three channels, so that the complexity of the encryption system can be effectively reduced without any reduction of its security. The principle of both encryption and decryption is detailed and the robustness of the system has been examined experimentally.
2、A new method for color image steganography using Discrete Quaternion Fourier Transforms(DQFT) is proposed. The host color image should be transformed to the DQFT domain, and the secret image should be encrypted first and then the encrypted color image can be embedded into the DQFT domain of the host image.
3、A new method for color image watermarking using Discrete Quaternion Cosine Transforms (DQCT) is proposed. The watermark image can be embedded in the DQCT domain of the host color image. Experimental results show that this method has good resistance to JPEG compression and is robust against Gaussian noise、salt & pepper noise and image scaling attack.
引文
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