离散余弦变换和全息技术相融合的图像压缩感知重构

为了获得理想的图像重构效果,提出一种基于离散余弦变换和全息技术相融合的图像重构算法。首先采用离散余弦变换对图像进行分解保留少数的低频分量,从而构建压缩感知的稀疏基加快重构速度,然后采用全息技术对图像重构结果进行处理,提高图像重构效果,最后采用仿真实验测试算法的性能。实验结果表明,相对于当前经典图像重构算法,本文算法不仅提高了图像重构质量,而且加快了图像重构速度,具有较好的实际应用价值。     

Image encryption using linear weighted fractional-order transform

As the linear weighted fractional-order Fourier transform (LWFRFT), an extension of the Fourier transform, has been widely studied, many linear weighted fractional-order transforms (LWFRTs) have been proposed consequently. Our research shows that the LWFRT has limitations when applied to image encryption. For example, its application to image encryption leads to the security risks of key invalidation. In this paper, we propose a new reformulation of the LWFRT which establishes the relation between many fractional-order transforms. With the help of the new reformulation, we point out the limitations of the LWFRT and analyze the reasons for key invalidation in image encryption. Finally, numerical simulation verifies our perspective.     

On the discrete cosine transform computation

A generalized signal flow graph for the forward and inverse discrete cosine transform (DCT) based on the Hou's recursive algorithm is described. The regular structure of the generalized signal flow graph enables to realize the DCT and inverse DCT computation for any given N = 2^m, m > 0, and is effectively implementable on a VLSI chip. Computer program for the DCT and inverse DCT computation is also presented.     

NEW FAST ALGORITHM OF 2-D DISCRETE COSINE TRANSFORM

In this paper, a new algorithm for the fast computation of a 2-D discrete cosine transform (DCT) is presented. It is shown that the N×N DCT, where N = 2m, can be computed using only N 1-D DCT's and additions, instead of using 2N 1-D DCT's as in the conventional row-column approach. Hence the total number of multiplications for the proposed algorithm is only half of that required for the row-column approach, and is also less than that of most of other fast algorithms, while the number of additions is almost comparable to that of others.     

TD-ERCS混沌系统和提升小波相结合的图像加密方法

为有效解决数字图像在通信传输中安全性的问题,提出了一种基于TD-ERCS混沌系统和提升小波理论相结合的数字图像加密方法.该方法首先对数字图像进行提升小波变换,得到数字图像的子带图像.然后,利用TD-ERCS混沌系统生成混沌序列对子带图像进行置换加密.数字图像的接受方在接收到加密的子带图像后,可以采用解密算法还原子带图像并在接收端重构原始数字图像.最后,对算法的安全性进行理论分析和计算机仿真.实验结果表 明,该方法对数字图像加密具有良好的安全性.     

基于矢量分解和相位截取Gyrator变换的图像加密

为了提高光学图像加密系统的安全性,采用了矢量分解和相位截取Gyrator变换进行图像加密。原始图像和随机相位函数叠加后做Gyrator变换,矢量分解将Gyrator变换域信息分解为一个随机相位函数和一个复函数。随机相位函数和复函数分别做不同变换角度的Gyrator变换后截取相位得到一个公钥和加密图像,截取振幅得到两个非对称相位密钥。进行了理论分析和数值验证,同时,设计了解密光学装置。结果表示:两个非对称相位密钥做为私钥,三个Gyrator变换角度做为额外密钥,这对增强系统的安全性是有帮助的。     

Image encryption method based on multiple-order fractional discrete Tchebichef transform and generating sequence

Fractional transform based image encryption methods have been widely studied in recent years.However,most of the existing fractional transform based image encryption methods are defined in the complex field.Thus,the encrypted images contain both phase and amplitude information,which is not conducive to transmission and storage.Moreover,some encryption methods that meet the requirements of reality-preserving have problems of relatively single keys,lacking of sensitivity and so on.An image encryption method was proposed based on multiple-order fractional discrete Tchebichef transform and generating sequence.The proposed method used randomly generated row and column vectors and generating sequence generated by Chaotic sequences as keys to encrypt images,which not only satisfied property of reality-preserving transmission but also greatly expanded the key space.The experimental results further demonstrate that the proposed encryption method can resist a variety of attacks,and decrypted images are almost non-distored,which indicate excellent encryption effect,sufficient security and robustness of the method.     

利用离散余弦变换的语音信号压缩方案

利用离散余弦变换后的语音信号能量主要集中在低频段的特点以及语音信号的短时平稳性，研究三种基于一维离散余弦变换的语音压缩方案。Matlab仿真结果表明三种方案的数据压缩率高，重建语音信号具有艮好的清晰度和自然度。     

A new optimal digital halftoning technique based on the discrete cosine transform

Digital halftoning is a technique to display a gray-level image with a bilevel device. Conventionally, most halftoning techniques are done in the spatial domain. A new halftoning technique based on the discrete cosine transform is proposed. The method chooses an optimal bilevel image to display the original gray-level image and minimize the weighted mean square error based on the discrete cosine transform domain. The simulation results indicate that our algorithm can produce very good halftoned images without false contours.     

一种基于分数傅立叶变换的图像加密技术

本文基于分数傅立叶变换的多样性,通过不同级次的分数傅立叶变换与谱变换相结合,提出了一种新的光学图像加密算法。经计算机模拟验证,此算法确实可行可靠。     

Patch based image denoising using the finite ridgelet transform for less artifacts

Patch based denoising methods have proved to lead to state-of-the-art results. However, in contrast with intensive pursuing of higher peak signal to noise ratio (PSNR), less attention is paid to visual quality improvement of denoised images. In this paper, we first compare the denoising performance in edge and smooth regions. Results reveal that edge regions are the main source for potential performance improvement. This motivates us to investigate the use of the finite ridgelet transform as a local transform for better preservation of directional singularities. A two stage denoising algorithm is then proposed to improve the representation of detail structures. Experimental results in denoising images which only contain white noise show that the proposed algorithm consistently outperforms other methods in terms of PSNR and Structural SIMilarity index. Denoised images by the proposed method also demonstrate good visual quality with the least artifacts and fake structures in experiments on natural images.     

基于多方向像素连续折叠机制与Radon变换的图像加密算法

提出了基于多方向像素连续折叠机制与Radon变换的图像加密算法,从不同的方向、利用不同的像素扩散技术来加密明文,显著消除密文周期性.首先,对初始明文完成均等分割,获取左、右两个子块;引入Radon变换机制,对左、右子块进行0°～180°的Radon变换,获取对应的Radon投影谱图像;利用Arnold映射、引力模型分别混淆左、右子块的Radon谱图像,获取两个子置乱密文,将二者进行组合,输出完整的置乱图像.为了从空间多个方向来扩散像素,设计了4个方向连续折叠机制,利用4个不同方向对应的扩散函数来改变像素值,实现图像加密.实验结果表明,与当前图像加密技术相比,所提算法具有更高的安全性与抗攻击能力,输出密文的像素分布更加均匀.     

基于小波包变换的分数阶光学加密技术研究

提出一种基于小波包变换(WPT)的分数阶光学图 像加密方法。利用WPT能够对图像多层次分解的特性,结合分数傅里叶变换(FRFT)的灵活性 ,将双随机相位、小波函数的类型及尺度因子和分数阶次作为密钥, 实现了图像的多重密钥加解密。同时,实现了图像小波域上的选择性加密,使加密样式变得 更灵 活多样,还增强了加密图像的抵抗恶意的攻击能力。数值模拟了加密和解密过程,分析了加 密效果和解密图像质量,验证了本文方法的可行性。     

基于Shear变换的彩色地形图混沌加密算法

针对目前研究地形图图像加密算法较少,以及现有图像加密算法易被破解的问题,提出基于Shear变换的彩色地形图混沌加密算法。该算法充分利用了Shear变换的多方向性,能够很好地对地形图的线划要素信息进行置乱的特点,以及Lorenz混沌系统具有极强初值敏感性和更大的密匙空间和安全性的特点。通过对彩色地形图的加密和解密实验,以及抗攻击性能对比实验,表明使用该算法加密后的彩色地形图具有更高的安全性,并且载体图像具有较高的抗攻击性能。     

Image encryption based on compressed sensing and DNA encoding

An image encryption scheme based on a four-wing hyperchaotic system combined with compressed sensing and DNA coding is proposed. The scheme uses compressed sensing (CS) to reduce the image according to a certain scale in the encryption process. The measurement matrix is constructed by combining the Kronecker product (KP) and chaotic system. KP is used to extend the low-dimensional seed matrix to the high-dimensional measurement matrix. The dimensional seed matrix is generated by a four-wing chaotic system. At the same time, the chaotic sequence generated by the chaotic system dynamically controls the DNA coding and then performs the XOR operation. Simulation experiments and performance analysis show that the algorithm has good performance and security.     

基于图像置乱技术融合FRFT的光学图像加密

针对二维图像加密系统的安全性问题,本文提出一种融合分数傅里叶变换和图像置换技术的光学图像加密方案。首先,使用jigsaw变换算法将原始图像分解成若干子图,并随机平移子图;然后,利用Arnold变换对图像像素进行置乱;最后,采用分数傅里叶变换加密置乱图像,并迭代重复这些过程。将jigsaw排列指标、Arnold频率和分数傅里叶阶等参数组成一个密钥空间,通过仿真实验在光学实现方面评估算法性能。实验结果表明,本文提出的方案具有很好的灵活性和鲁棒性。     

The fractional Fourier transform over finite fields

The central contribution of this paper is the definition of the fractional Fourier transform over finite fields (GFrFT). In order to introduce the GFrFT, concepts related to trigonometry in finite fields are reviewed and some new ideas put forward. In particular, graphic representations of elements in a finite field are suggested and analogies with real and complex numbers are discussed. A modified version of the finite field Fourier transform is given and its eigenstructure is analyzed. This allows us to develop GFrFT theory and investigate its main characteristics. Some illustrative examples are also given throughout the paper.     

基于分数傅立叶变换和相位恢复算法的彩色图像加密

提出一种基于分数傅立叶变换和相位恢复算法的彩色图像加密技术。加密时把待加密彩色图像分解为红（R）、绿（G）、蓝（B）三个分量,并构成联合图,然后将联合图迭代编码到两块相位板中,在迭代过程中,同时改变两块相位板。解密时,只需要将编码得到的两块相位板匹配起来放在正确的位置,就可以恢复出高质量的彩色图像。模拟实验表明,该算法收敛速度快,系统安全性能高,并且可以光学实现。     

基于离散余弦变换和主成分分析的光照条件人脸识别

在光照变化条件下,人脸识别的正确率急剧下降,为了解决该难题,提出了一种离散余弦变换和主成分分析相融合的光照变化条件人脸识别方法.首先对人脸图像进行分块,并采用离散余弦变换对每一个子块提取DCT系数,然后采用主成分分析提取人脸特征,并采用深度学习算法建立人脸识别的分类器,最后采用ORL和Yale B人脸库进行仿真实验,测试其有效性和优越性.实验结果表明,相比其它光照人脸识别方法,本文方法提高了光照人脸图像的识别率,消除了光照变化的不利影响,具有较强的鲁棒性.