Constructing symmetric nonnegative matrices via the fast fourier transform

We derive an algorithm based on the fast Fourier transform to construct a real symmetric matrix S with eigenvalues λ₁≥λ₂≥⋯≥λ_n, with eigenvector e = [1, 1, … ,1]^T belonging to the eigenvalue λ₁.We find simple conditions on the eigenvalues such that the algorithm constructs an irreducible matrix S = λ₁E, where E is a symmetric doubly stochastic matrix.     

Dual convolutional codes and the MacWilliams identities

A recursion for sequences of spectra of truncated as well as tailbitten convolutional codes and their duals is derived. The order of this recursion is shown to be less than or equal to the rank of the weight adjacency matrix (WAM) for the minimal encoder of the convolutional code. It is sufficient to know finitely many spectra of these terminated convolutional codes in order to obtain an infinitely long sequence of spectra of their duals.     

四元数表示和NSCT变换的彩色人脸图像识别

将彩色人脸图像用四元数实矩阵的形式表示,对该矩阵作多级非抽样Contourlet（Nonsubsampled Contourlet,NSCT）变换,在各子带系数上作奇异值分解,进而获得图像的代数特征向量,由神经网络训练和识别。实验结果表明,该方法可以有效地提高彩色人脸图像的识别率,是一种有效的彩色人脸识别方法。     

基于混沌数列变换的图像加密算法

针对现有的数字图像加密算法存在算法复杂、运算成本大以及安全性不高等问题,提出了一种基于混沌数列变换的数字图像加密算法.该算法通过对Logistic和Hybrid两种不同的混沌序列进行变换,从像素灰度值以及像素位置两方面对图像进行加密.实验结果表明,该算法加密效果良好并且能够抵御统计分析以及攻击操作,密钥量大安全性高,符合现代技术对图像加密的要求.     

序列捕获的序列核变换方法

在序列扩频、加扰通信系统中,通常采用连续接收信号并进行滑动相关运算的方法,通过搜索相关峰进行序列捕获,需要接收多个完整周期的序列。随着序列周期的加大,一方面需要花费大量的接收端存储资源,另一方面,相关运算的计算开销会呈指数增长,导致很难实时捕获长周期序列。为解决这一问题,提出了一种序列核变换方法,变换后的每个元素均包含有完整的序列信息,实现了序列信息压缩。然后,基于该变换方法将捕获过程分为序列检测和序列捕获两个阶段,只在检测到目标序列后才开始捕获,进一步降低了计算开销。理论分析和仿真验证表明,算法通过牺牲部分低信噪比环境下的捕获成功率换取了计算资源的大量减少,算法可在一个序列周期内快速捕获不同周期的m序列,并且所节省的计算资源随序列周期变大而增多。     

累积量测序列的区间云变换及识别

目标多属性序列类数据不能直接与数据库中的区间类数据融合识别, 对此, 提出一种基于云变换的序列-区间异类数据识别算法. 对目标多属性序列数据进行频数计算形成频率分布函数, 并进行虚警检测, 实施云变换形成云簇, 提取云簇特征, 再根据3 En 准则形成云滴区间, 实现了序列型数据的区间化表示. 进一步, 利用一种区间多属性识别判定准则进行识别判定, 得到识别结果, 解决了序列-区间异类数据的识别问题. 仿真实验结果验证了该算法对序列-区间异类数据识别的有效性.

     

Discrete fractional Fourier transform based on the eigenvectors of tridiagonal and nearly tridiagonal matrices

The recent emergence of the discrete fractional Fourier transform (DFRFT) has caused a revived interest in the eigenanalysis of the discrete Fourier transform (DFT) matrix F with the objective of generating orthonormal Hermite–Gaussian-like eigenvectors. The Grünbaum tridiagonal matrix T—which commutes with matrix F—has only one repeated eigenvalue with multiplicity two and simple remaining eigenvalues. A detailed eigendecomposition of matrix T is performed with the objective of deriving two orthonormal eigenvectors—common to both the F and T matrices—pertaining to the repeated eigenvalue of T. The nearly tridiagonal matrix S first introduced by Dickinson and Steiglitz and later studied by Candan et al.—which commutes with matrix F—is rigorously proved to reduce to a 2×2 block diagonal form by means of a similarity transformation defined in terms of an involutary matrix P. Moreover explicit expressions are derived for the elements of the two tridiagonal submatrices forming the two diagonal blocks in order to circumvent the need for performing two matrix multiplications. Although matrix T has the merit of being tridiagonal and does not need the tridiagonalization step as matrix S, the simulation results show that the eigenvectors of matrix S better approximate samples of the Hermite–Gaussian functions than those of matrix T and moreover they have a shorter computation time due to the block diagonalization result. Consequently they can serve as a better basis for developing the DFRFT.     

自适应小波变换的混沌扩频数字水印

在分析了自适应小波变换和扩频特性关系的基础上,研究了混沌序列扩频特性,并提出一种基于自适应小波变换的混沌扩频数字水印算法.利用该算法,可实现混沌扩频图像数字水印的嵌入和提取.计算机模拟实验表明该方法具有较好的不可视性、鲁棒性,并且可以实现扩频数字水印的盲检测性.     

The relationship between the Laplace transform and Fourier transform

In this note, a relationship between the one-sided Laplace transform and the one-sided Fourier transform is discussed.     

The boundary trace transform: An edge and region enhancement transform

The boundary trace transform (BTT) is an edge enhancing procedure which is independent of thresholds based on iso-density contours. It may therefore sometimes be employed to produce useful boundaries of objects where global level slicing fails. It is particularly applicable in the broad class of biological images which characteristically poorly defined or in which heavily textured regions locally obscure subobject contrast. contain several cells of different types. This is the case where subobject boundaries are A variation of the BTT is useful for finding large textured subobjects within differently textured darker subobjects.     

The Trace transform and its applications

The Trace transform proposed, a generalization of the Radon transform, consists of tracing an image with straight lines along which certain functionals of the image function are calculated. Different functionals that can be used may be invariant to different transformations of the image. The paper presents the properties the functionals must have in order to be useful in three different applications of the method: construction of invariant features to rotation, translation and scaling of the image, construction of sensitive features to the parameters of rotation, translation and scaling of the image, and construction of features that may correlate well with a certain phenomenon we wish to monitor     

The adaptive hough transform

We introduce the Adaptive Hough Transform, AHT, as an efficient way of implementing the Hough Transform, HT, method for the detection of 2-D shapes. The AHT uses a small accumulator array and the idea of a flexible iterative "coarse to fine" accumulation and search strategy to identify significant peaks in the Hough parameter spaces. The method is substantially superior to the standard HT implementation in both storage and computational requirements. In this correspondence we illustrate the ideas of the AHT by tackling the problem of identifying linear and circular segments in images by searching for clusters of evidence in 2-D parameter spaces. We show that the method is robust to the addition of extraneous noise and can be used to analyze complex images containing more than one shape.     

The secure wavelet transform

There has been an increasing concern for the security of multimedia transactions over real-time embedded systems. Partial and selective encryption schemes have been proposed in the research literature, but these schemes significantly increase the computation cost leading to tradeoffs in system latency, throughput, hardware requirements and power usage. In this paper, we propose a light-weight multimedia encryption strategy based on a modified discrete wavelet transform (DWT) which we refer to as the secure wavelet transform (SWT). The SWT provides joint multimedia encryption and compression by two modifications over the traditional DWT implementations: (a) parameterized construction of the DWT and (b) subband re-orientation for the wavelet decomposition. The SWT has rational coefficients which allow us to build a high throughput hardware implementation on fixed point arithmetic. We obtain a zero-overhead implementation on custom hardware. Furthermore, a Look-up table based reconfigurable implementation allows us to allocate the encryption key to the hardware at run-time. Direct implementation on Xilinx Virtex FPGA gave a clock frequency of 60 MHz while a reconfigurable multiplier based design gave a improved clock frequency of 114 MHz. The pipelined implementation of the SWT achieved a clock frequency of 240 MHz on a Xilinx Virtex-4 FPGA and met the timing constraint of 500 MHz on a standard cell realization using 45 nm CMOS technology.     

The vector-gradient Hough transform

The paper presents a new transform, called vector-gradient Hough transform, for identifying elongated shapes in gray-scale images. This goal is achieved not only by collecting information on the edges of the objects, but also by reconstructing their transversal profile of luminosity. The main features of the new approach are related to its vector space formulation and the associated capability of exploiting all the vector information of the luminosity gradient     

一种新的基于三维小波变换的序列图像编码算法

介绍了由时间轴一维与帧内二维组合而成的准三维小波变换结合运动补偿的编码器结构，并针对运动变化较缓慢的序列图像，观察实验数据特点，提出了改进零树编码与像素点编码相结合的编码策略。计算机仿真实验证明，采用该方法，可有效降低计算复杂度，提高执行效率，同时在压缩比达到400∶1时，图像恢复质量仍在29dB 以上。     

基于Curvelet变换的浮选泡沫图像序列时空联合去噪

提出一种时空信息联合的浮选泡沫图像去噪方法。首先,将基于GSM统计建模和贝叶斯最小二乘准则的局部空间去噪方法应用到图像Curvelet域,获得基于单图像信息的Curvelet空间域最佳系数估计;然后,根据运动补偿原理和帧间子块的相关性引入帧间加权因子,通过加权处理帧间子块系数获得待处理图像时空相关的最佳去噪系数估计。结果表明,该方法能在去除噪声的同时更好地保护泡沫的细节,对于严重噪声污染的泡沫图像序列也能获得较好的处理效果。     

环F2+vF2上线性码的MacWilliams恒等式*

定义了环F2 vF2上码字的李重量分布的概念,利用域F2上线性码和对偶码的重量分布的关系及gray映射,给出了该环上线性码与对偶码之间各种重量分布的MacWilliams恒等式。