彩色图像超复数空间的自适应水印算法

 针对彩色载体图像,本文提出了一种超复数频域的自适应水印算法,它首先对彩色载体图像进行快速超复数傅氏变换,在超复数频谱实部选择合适频段的基础上,再利用人类视觉系统对彩色载体图像的纹理、边缘和亮度的掩蔽特性,对选择的频段赋予不同的掩蔽强度而嵌入水印,从而在超复数频域内实现了一种彩色载体图像自适应的水印算法.实验结果表明,通过彩色图像的自适应掩蔽,大大提高了超复数频域水印算法的不易感知性和鲁棒性,且抗攻击性能也优于无自适应掩蔽的超复数频域水印算法;和现有文献的比较结果验证了本算法的这些优越性.     

客观评估彩色图像质量的超复数奇异值分解法

本文利用超复数直接对彩色图像建模,保存了彩色图像完整的信息;基于超复数奇异值分解(也称四元数奇异值分解QSVD)提出一种全新的图形化与数值化相结合的彩色图像质量评估测度,不仅能判断图像失真等级,还能判断不同的失真类型.测试结果表明,本文提出的算法比传统的MSE、PSNR以及MSSIM等算法性能更优.     

改善复数LMS算法收敛性能的方法

在分析复数LMS算法内部信号流程的基础上,指出复数LMS算法存在梯度噪声交叉耦合干扰的特性,提出对复数LMS算法应该分实部和虚部独立调整学习步长,并具体给出了一种复数LMS算法的变步长方法.仿真实例支持了本理论的分析结论,并证实了所提出的变步长方法的有效性.     

复数域非线性扩散滤波在图像处理中的应用

图像处理中去噪和边缘保持是一对矛盾体,去噪滤波经常会失去高频部分的信号,而边缘信息主要以高频信息为主.考虑了一种新的方法——复数域非线性扩散方法,该方法通过结合自由薛定谔方程将传统各向异性扩散方程拓展到复数域,复数域实部信号可以很好地滤波,将复数域扩散项虚部加入shock滤波器,该方法克服了传统的边缘检测方法边缘保持能力差的缺点.试验结果表明:该算法具有良好的抗噪性和边缘细节的保持性,边缘检测效果良好.     

基于复数网络与注意力机制的信号调制识别

通信信号调制识别作为管理、监测电磁频谱的重要手段,具有重要的研究价值和应用前景。本文利用调制信号的频域信息,提出一种基于复数神经网络的信号调制识别方法。首先将I、Q两路信号组合成复信号,经过快速傅里叶变换(FFT)后把得到的实部和虚部组合起来作为输入网络的数据集。其次,设计了一种复数神经网络结构,并引入了注意力机制对网络结构进行改良。仿真结果表明,本文提出的方法可以有效识别9种调制方式,在信噪比为6 dB时,平均正确识别率达到96.33%。     

低信噪比下二维联合快速超分辨B-ISAR成像方法

双基地ISAR成像分辨率受限于信号带宽和方位积累时间,且成像质量受噪声影响严重.本文在充分考虑回波的二维联合稀疏特征基础上,提出二维联合字典下的矩阵复数近似消息传递超分辨快速成像算法.在构建双基地ISAR的二维联合超分辨成像模型基础上,首先通过向量化处理,将二维超分辨成像问题转换为复数基追踪去噪问题;其次通过两种策略实现复数基追踪去噪问题的快速求解,一是利用向量化与Kronecker积的关系,推导出矩阵形式复数近似消息传递算法,从而避免向量化处理带来的大矩阵运算量和大存储量问题;二是为进一步减少单次迭代的运算量,将矩阵乘法等效为二维快速傅里叶变换.最后,利用本文算法在迭代过程中对噪声阈值不断精确逼近,提高算法在低信噪比下的成像能力.仿真数据成像结果验证了本文算法的有效性.     

超复数域小波变换的显著性检测

针对现有频域显著性检测方法得到的显著区域不完整的问题,该文提出一种多尺度分析的频率域显著性检测方法。首先由输入图像特征通道信息构建4元超复数,然后通过小波变换对4元超复数域中幅度谱进行多尺度分解,计算生成多尺度下的视觉显著图,最后由评价函数选出效果较好显著图合成最终视觉显著图。实验结果表明,该文方法能够有效地抑制背景干扰,快速、精确地找到完整的显著目标,具有较高的检测精确度。     

简化的复数非圆信号广义线性盲均衡算法

为了提高复数非圆信号的盲均衡性能,本文深入分析广义线性滤波理论,利用常模准则的简便性和稳健性,针对低阶复数非圆信号构造了简化的广义线性盲均衡器,并提出了一种简化的广义线性递归最小二乘常模盲均衡算法。简化的广义线性盲均衡器直接利用接收信号的实部和虚部作为均衡器输入,从而得到接收信号完整的实部和虚部的二阶统计量信息。新算法将标准的广义线性均衡算法的复数运算变成实数运算,有效地降低了标准广义线性均衡器的复杂度。仿真实验结果表明,与传统常模盲均衡算法相比,新算法在不提高计算复杂度的基础上,能够有效降低剩余码间干扰和误码率。      

时谐场和复数场的对应研究

电磁时谐场的复数表示理论,其基础在于对应,即电磁一次量的实部(或虚部)对应时谐场量.这种方法简单明了,因此获得了广泛的应用.然而必须提出,电磁二次量的复数表示并不能从能量定理的普遍形式导出[6],因此不少文献[3-5]均避免给出复Poynting定理.本文提出了时谐场二次量的复数表示的对应定理,并探讨其中各项的相关意义,从而使复Poynting定理,Foster定理和Lorentz定理有了坚实的基础.     

四元数和超复数在二维二次非线性相位耦合分析中的应用

针对二维二次非线性相位耦合分析中的分维配对问题,本文首先对一般二维谐波信号模型进行变换,构造了符合四元数结构的新的信号模型.接着讨论了Hamilton四元数、三维超复数及"新四元数"在估计二维谐波频率中的可能性.最后根据上述模型利用特殊的三阶累积量切片分析了加性高斯有色噪声中二维二次非线性相位耦合及联合Hamilton四元数和超复数在二维二次非线性相位耦合中的应用前景.此方法避免了在复数模型的二维二次非线性相位耦合分析中构造复杂的增广矩阵,并从根本上解决了通过分维求取频率之后,频率配对中所有可能产生的错误频率对,以及有可能产生的两维频率估计精度的不平衡性.仿真实验验证了本文的理论.     

Hypercomplex Fourier transforms of color images.

Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed.     

Estimation of Motions in Color Image Sequences Using Hypercomplex Fourier Transforms

Although the motion estimation problem has been extensively studied, most of the proposed estimation approaches deal mainly with monochrome videos. The most usual way to apply them also in color image sequences is to process each color channel separately. A different, more sophisticated approach is to process the color channels in a “holistic” manner using quaternions, as proposed by Ell and Sangwine. In this paper, we extend standard spatiotemporal Fourier-based approaches to handle color image sequences, using the hypercomplex Fourier transform. We show that translational motions are manifested as energy concentration along planes in the hypercomplex 3-D Fourier domain and we describe a methodology to estimate the motions, based on this property. Furthermore, we compare the three-channels-separately approach with our approach and we show that the computational effort can be reduced by a factor of 1/3, using the hypercomplex Fourier transform. Also, we propose a simple, accompanying method to extract the moving objects in the hypercomplex Fourier domain. Our experimental results on synthetic and natural images verify our arguments throughout the paper.      

结合Fourier变换对称性和随机多分辨率奇异值分解的彩色图像加密

提出一种基于Fourier变换对称性和随机多分辨率奇异值分解(R-MRSVD)的彩色图像加密算法。首先计算归一化明文图像的平均值作为logistic-exponent-sine映射的初值,并生成随机矩阵和位置索引;然后对每个颜色通道分别进行二维离散Fourier变换,根据共轭对称性仅保留一半的频谱系数,并提取实部分量和虚部分量构建实数矩阵;最后对实数矩阵进行R-MRSVD和Josephus置乱操作,得到密文图像。将明文图像的像素特征作为混沌序列的初值,保证算法具有高敏感性和高安全性,同时实值的密文便于存储和传输。对算法的解密图像质量、统计特性、密钥敏感性、抗选择明文攻击、鲁棒性等性能进行测试,仿真结果表明,所提加密算法具有可行性和安全性。     

Robust multiple color images encryption using discrete Fourier transforms and chaotic map

Based on discrete Fourier transforms and logistic-exponent-sine map, this paper investigates an encryption algorithm for multiple color images. In the encryption process, each color image represented in trinion matrix is performed by block-wise discrete trinion Fourier transforms. Then the first real matrix is constructed by splicing real and imaginary parts of transformed results. Followed by two-dimensional discrete Fourier transform, the second real matrix is synthesized only using half of the spectrum on the basis of the conjugate symmetry property. In order to further enhance the randomness of interim result, the random multi-resolution singular value decomposition is exploited. Afterwards, a sharing process is utilized to get final cipherimages. Numerical simulations performed on 300 color images have shown that quality of correctly decrypted images is much better, where the PSNR value is up to 305.03 dB. The number of changing pixel rate and unified average changing intensity are respectively greater than 99.99% and 33.33%, indicating good sensitivity. The comparison with other methods under noise and cropping attacks validates the reliability of the proposed algorithm.     

Parallel vector processing of multidimensional orthogonal transforms for digital signal processing applications

This paper presents vector and parallel algorithms and implementations of one- and two-dimensional orthogonal transforms. The speed performances are evaluated on Cray X-MP/48 vector computer. The sinusoidal orthogonal transforms are computed using fast real Fourier transform (FFT) kernel. The non-sinusoidal orthogonal transform algorithms are derived by using direct factorizations of transform matrices. Concurrent processing is achieved by using the multitasking capability of Cray X-MP/48 to transform long data vectors and two-dimensional data vectors. The discrete orthogonal transforms discussed in this paper include: Fourier transform (DFT), cosine transform (DCT), sine transform (DST), Hartley transform (DHT), Walsh transform (DWHT) and Hadamard transform (DHDT). The factors affecting the speedup of vector and parallel processing of these transforms are considered. The vectorization techniques are illustrated by an FFT example.This work is supported in part by the National Science Foundation, Pittsburgh Supercomputing Center (grant number ECS-880012P) and by the PEW Science Education Program.     

Envelope detection using generalized analytic signal in 2D QLCT domains

The hypercomplex 2D analytic signal has been proposed by several authors with applications in color image processing. The analytic signal enables to extract local features from images. It has the fundamental property of splitting the identity, meaning that it separates qualitative and quantitative information of an image in form of the local phase and the local amplitude. The extension of analytic signal of linear canonical transform domain from 1D to 2D, covering also intrinsic 2D structures, has been proposed. We use this improved concept on envelope detector. The quaternion Fourier transform plays a vital role in the representation of multidimensional signals. The quaternion linear canonical transform (QLCT) is a well-known generalization of the quaternion Fourier transform. Some valuable properties of the two-sided QLCT are studied. Different approaches to the 2D quaternion Hilbert transforms are proposed that allow the calculation of the associated analytic signals, which can suppress the negative frequency components in the QLCT domains. As an application, examples of envelope detection demonstrate the effectiveness of our approach.     

Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for Real DFTs

In this paper, we systematically derive a large class of fast general-radix algorithms for various types of real discrete Fourier transforms (real DFTs) including the discrete Hartley transform (DHT) based on the algebraic signal processing theory. This means that instead of manipulating the transform definition, we derive algorithms by manipulating the polynomial algebras underlying the transforms using one general method. The same method yields the well-known Cooley-Tukey fast Fourier transform (FFT) as well as general radix discrete cosine and sine transform algorithms. The algebraic approach makes the derivation concise, unifies and classifies many existing algorithms, yields new variants, enables structural optimization, and naturally produces a human-readable structural algorithm representation based on the Kronecker product formalism. We show, for the first time, that the general-radix Cooley-Tukey and the lesser known Bruun algorithms are instances of the same generic algorithm. Further, we show that this generic algorithm can be instantiated for all four types of the real DFT and the DHT.     

Multichannel transforms for signal/image processing

This paper presents a novel approach to the Fourier analysis of multichannel time series. Orthogonal matrix functions are introduced and are used in the definition of multichannel Fourier series of continuous-time periodic multichannel functions. Orthogonal transforms are proposed for discrete-time multichannel signals as well. It is proven that the orthogonal matrix functions are related to unitary transforms (e.g., discrete Hartley transform (DHT), Walsh-Hadamard transform), which are used for single-channel signal transformations. The discrete-time one-dimensional multichannel transforms proposed in this paper are related to two-dimensional single-channel transforms, notably to the discrete Fourier transform (DFT) and to the DHT. Therefore, fast algorithms for their computation can be easily constructed. Simulations on the use of discrete multichannel transforms on color image compression have also been performed.