采用离散余弦变换的小波图像去噪方法

提出一种通过对小波域中噪声能量的估计来进行去噪的新方法。算法采用离散余弦变换(DCT)提取小波系数的主要特征,无需对噪声方差进行估计。对图像进行小波分解,利用 DCT对高频子带进行局部特征提取;利用部分 DCT 系数对小波系数进行重建,并以重建系数的平均能量作为局部噪声能量的估计;去除原小波系数中的噪声分量后,进行小波逆变换,得到去噪后的图像。实验证明,其峰值信噪比(PSNR)比通常的阈值萎缩法提高了 2-4dB。     

Directional textures auto-inspection using discrete cosine transform

This paper describes a global image restoration scheme using a discrete cosine transform (DCT) that can be used to detect defects in directional textured surfaces automatically. The input spatial domain image is first transformed into the DCT domain so that the dominant directions of the texture in the input image will be compacted into the orthogonal straight lines or impulses through the direct current (DC) component of the spectrum. The linear primitives associated with the high-energies in the DCT domain are eliminated by reducing them to zero before transforming back to the spatial domain. Finally, the defects, if any, are extracted by the thresholding method. Experiments on a variety of product surfaces with directional textures such as straight, slanted, orthogonal, slanted orthogonal, and oblique linear primitives were conducted in this paper. The proposed scheme would blur directional textures and preserved only local defects if they were initially embedded in the image. Furthermore, some preliminary experiments were also conducted to demonstrate the proposed scheme was insensitive to horizontal and vertical shifting, changes in illumination, and image rotation.     

茶叶近红外光谱数据的离散余弦变换压缩方法

利用离散余弦变换具有的去相关能力,通过引入阈值和保留能量来定量描述茶叶近红外光谱数据 离散余弦变换后的特性.结果表明,离散余弦变换对近红外光谱具有较强的压缩能力。     

Image encryption based on a reality-preserving fractional discrete cosine transform and a chaos-based generating sequence

A novel image encryption technique based on a reality-preserving fractional discrete cosine transform (FrDCT) and a chaos-based generating sequence is proposed. The FrDCT is a generalization of the discrete cosine transform (DCT). This reality-preserving FrDCT inherits the virtues of both the DCT and fractional transform, providing improved security and flexibility by employing the generating sequence as an extra key in addition to the fractional orders. The most fascinating advantage of the FrDCT is its reality-preserving property, which ensures real ciphertext for real plaintext, which is conducive to display, storage, and transmission. Performance and security analysis demonstrates that this algorithm is valid, secure, sensitive to keys, and robust to noise and occlusion attacks.     

离散余弦小波包变换及语音信号压缩感知

针对语音信号压缩感知问题,在研究语音离散余弦变换(Discrete Cosine Transform,DCT)系数和小波包变换(Wavelet Packet Transform,WPT)特性的基础上构造了离散余弦小波包变换(Discrete Cosine Wavelet Packet Transform,DCWPT)。DCWPT首先获取语音信号的DCT域系数,结合语音频谱特性选取部分DCT系数进行WPT变换,从而得到比DCT系数更加稀疏的DCWPT系数。为将此变换直接用于压缩感知,构造了DCWPT的正交稀疏分解矩阵并分析了其稀疏表示性能。结合稀疏表示基优化了正交匹配追踪重构算法,提出了基于DCWPT的语音信号压缩感知框架。通过压缩重构对照实验,采用主客观评价指标,得出该方法优于传统基于DCT的语音压缩感知方法的结论。     

High compressive ghost imaging method based on discrete cosine transform using weight coefficient matching

ABSTRACT

Ghost imaging can capture a scene without directly catching sight of the target, but in the case of high compression ratio, high-quality imaging is challenging at present. Here a ghost imaging method using weight coefficient matching based on discrete cosine transform (DCT) is proposed, in which the high-quality target images can be retrieved by obtaining the larger weight value in one-dimensional (1D) DCT spectrum. In the case of low sampling, the proposed method can not only acquire the spectral coefficients with large weight, but also put them in the correct position; eventually it can obtain the desired image by inverse discrete cosine transform of the spectrum. At the same sampling ratio, both simulation results and optical experiments show that the reconstructed image quality of the proposed method exhibits better performance. In addition, even the sampling ratio is as low as about 3%, the outline of the target image can still be roughly recognized.     

Image encryption scheme based on random fractional discrete cosine transform and dependent scrambling and diffusion

An image encryption scheme is proposed by combining the random fractional discrete cosine transform (RFrDCT) with the dependent scrambling and diffusion (DSD). The application of the randomization, irrational choice and vectorization of fractional orders and the randomization of generating sequences improves the key-sensitivity and thus enlarges the key space greatly. Both the locations and the values of RFrDCT transformed coefficients are changed during the stage of DSD to further enhance the security of image encryption scheme. Numerical simulations demonstrate that the proposed image encryption scheme is feasible, secure and capable of resisting common classical attacks.     

线性正则正弦与余弦变换的卷积定理及其应用

针对奇、偶信号的去噪问题,提出了一种基于线性正则正(余)弦变换卷积定理的乘性滤波器设计方法。在现有线性正则变换域卷积理论的基础上,研究了两类线性正则正(余)弦变换卷积定理,利用所得卷积定理,通过合理选择滤波函数,设计了一类基于卷积定理的线性正则正(余)弦变换域带限信号的乘性滤波模型,并对算法的复杂度进行分析。研究表明,这种滤波模型特别适合处理奇、偶信号,并能有效降低乘积滤波的计算复杂度,提高运算效率。     

傅里叶变换同轴数字全息记录余弦变换谱系数

余弦变换广泛应用于图像和视频的压缩编码以及模式识别之中。余弦变换为实偶对称的傅里叶变换,把实偶对称物体传送到位于傅里叶变换透镜前焦面的空间光调制器上,采用单色均匀平面激光光波照射,则在后焦面上为光波复振幅分布为实偶对称物体的傅里叶变换,即为物体的余弦变换。由于余弦变换谱系数既有正实数又有负实数,提出了采用傅里叶变换同轴数字全息方法记录余弦变换谱系数,通过把数字全息图减去参考光光强和物光光强而得到余弦变换系数。理论推导和实验结果表明了该方法的可行性,该方法可应用于图像的快速余弦变换。     

Optimum design of structures against earthquake by discrete wavelet transform

Optimum design of structures is achieved by a modified genetic algorithm. Some features of the simulated annealing are used to control various parameters of the genetic algorithm. The loads are considered as earthquake loads. A time history analysis is carried out for the dynamic analysis. To decrease the computational work of analysis, a discrete wavelet transform is used by which the number of points in the earthquake record is reduced. Then in the optimization process, the structures are analysed with these points. To reconstruct the actual responses of structures from the responses of these points, a reverse wavelet transform is employed. A number of structures are designed for minimum weight and the results are compared with optimal solution using exact dynamic analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Mathematical models for prediction of active substance content in pharmaceutical tablets and moisture in wheat

In the prediction of active substance content in pharmaceutical tablets and moisture in wheat, a very large number of wavelengths were used. Hence, a method to identify a limited number of wavelengths was developed. We introduce a novel approach that uses the discrete cosine transform (DCT) for this purpose. The data was obtained using near infrared spectrometer. From the DCT coefficients, a limited number was chosen as predictor variables to be used in partial least square (PLS) regression. Likewise, a limited number of DFT coefficients were also used in the PLS regression. The performance of combining the DCT with PLS was compared with that of the PLS model using the full spectral data and with the discrete Fourier transform (DFT). The results showed that the PLS model using DCT coefficients produced lower root mean square error than using the full NIR spectral data with the PLS and also the DFT.     

Improved upper complexity bounds for the discrete fourier transform

The linear complexityL ₂ (G) of a finite groupG is the minimal number of additions, subtractions and multiplications by complex constants of absolute value 2 sufficient to evaluate a suitable Fourier transform of G. Combining and modifying several classical FFT-algorithms, we show thatL ₂(G)8|G|log₂|G| for any finite metabelian groupG.     

Pricing financial claims contingent upon an underlying asset monitored at discrete times

Exotic option contracts typically specify a contingency upon an underlying asset price monitored at a discrete set of times. Yet, techniques used to price such options routinely assume continuous monitoring leading to often substantial price discrepancies. A brief review of relevant option-pricing methods is presented. The pricing problem is transformed into one of Wiener–Hopf type using a z-transform in time and a Fourier transform in the logarithm of asset prices. The Wiener–Hopf technique is used to obtain probabilistic identities for the related random walks killed by an absorbing boundary. An accurate and efficient approximation is obtained using Padé approximants and an approximate inverse z-transform based on the trapezoidal rule. For simplicity, European barrier options in a Gaussian Black–Scholes framework are used to exemplify the technique (for which exact analytic expressions are obtained). Extensions to different option contracts and options driven by other Lévy processes are discussed.     

广义特征值问题的快速傅里叶变换法

针对广义特征值问题提出离散傅里叶变换法。该方法把结构的动力响应看作是一种信号,利用快速傅里叶变换进行分析,从而得到结构的振动频率。该方法避免对刚度矩阵求逆,可同时计算出所有的特征值,是一种直接方法。数值算例验证了该方法的正确性。     

基于能量守恒全零DCT系数块的预先判别算法

针对全零DCT系数块,为避免对其进行变换和量化操作以减少编码器的运算量,从DCT公式、量化和能量守恒出发,在分析现有判别法对全零DCT系数块的误判与漏判的基础上,提出了一种预先判断全零DCT系数块的新方法,可应用于基于块的视频编码器中.同时,结合H.264整数变换和量化的特点对该算法进行了改进和仿真实验.实验结果表明,新提出的算法在保持PSNR不变的情况下,较现有典型方案有高出达32%的检出率,因而可更大幅度地降低DCT变换量化模块的计算复杂度.     

Weakly equilibrated basis functions for elasticity problems

In this paper weakly equilibrated basis functions (EqBFs) are introduced for the development of a boundary point method. This study is the extension of the one in (Int. J. Numer. Methods Engng. 81 (2010) 971–1018) using exponential basis functions (EBFs) which are available just for partial differential equations (PDEs) with constant coefficients. Here the EqBFs are evaluated numerically to solve more general PDEs with non-constant coefficients. The EqBFs are found through weighted residual integrals defined over a fictitious domain embedding the main domain. A series of Chebyshev polynomials are used for the construction of the basis functions. By properly choosing the weight functions as the product of two unidirectional functions, here with Gaussian distribution, the main 2D integrals are written as the product of the simpler 1D ones. The results of the integrals can be stored for further use; however in some particular cases the EqBFs may be stored as a set of library functions. The results may also be found useful for those who are interested in residual-free functions in other numerical methods. For the verification, we discuss on the validity of the solution through an essential and comprehensive test procedure followed by several numerical examples.     

采用双频光栅投影的快速傅里叶变换轮廓术

傅里叶变换轮廓术中通过反正切计算出的相位是截断的,如果被测物高度变化引起的相邻点的非截断相位变化过大,就无法直接进行正确的相位展开。故提出一种采用双频光栅的快速傅立叶变换轮廓术：从一帧条纹图中获取同一物体对应于不同等效波长的两组截断相位,先展开对应于低频的低精度截断相位,并以此为参考,根据双频光栅两个频率之间的关系,展开对应于高频的高精度相位。经过模拟比较,在误差范围内比传统方法恢复的图形有了较大的改善,相对误差率由2．26％下降到1．79％。     

Hough变换快速检测圆形PCB Mark

提出一种Hough变换检测圆形PCB(PrintedCircuitBoard,印刷电路板)Mark的方法。对检测图像进行阈值变换,并利用区域面积分割,将Mark区域和背景及噪声分离开来。计算Mark区域中心点,Hough变换圆心累加范围限制在这个中心点附近区域。依据Mark实际尺寸计算检测图像中Mark的半径,将累加器从三维降为二维。对检测图像进行Canny算子边缘检测后,采用先大间隔后小间隔的粗细累加策略,完成Hough变换检测。在全视觉贴片机SMT2505上应用表明,Mark中心检测误差和执行时间分别小于1个像素和50ms。继承了传统Hough变换检测精度高、抗噪能力强的优点,速度比传统Hough变换提高了2～3个数量级。     

An overview of LULU operators and discrete pulse transform for image analysis

Abstract

This paper presents an overview of LULU operators and discrete pulse transform (DPT). Data extraction from signals and images is a popular area of research. Different methods are being used for data extraction such as different types of linear and nonlinear operators. LULU operator is one of the most important rank selector nonlinear filters used for data analysis which is widely being used for signal analysis, especially in impulse noise filtering. It is computationally more efficient and the behaviour of the operator is simple to describe. Based on the composition of different orders of LULU operators, DPT on multi-resolution is defined, which describes the sequences into pulses with different magnitudes. DPT allows a multi-resolution measure of roughness of images and sequences. It is a powerful technique for image analysis and can also be used for the estimation of standard deviation of a random distribution.