A two-phase face recognition method in frequency domain

In this paper, we propose a two-phase face recognition method in frequency domain using discrete cosine transform (DCT) and discrete Fourier transform (DFT). The absolute values of DCT coefficients or DFT amplitude spectra are used to represent the face image, i.e. the transformed image. Then a two-phase face classification method is applied to the transformed images. This method is as follows: its first phase uses the Euclidean distance formula to calculate the distance between a test sample and each sample in the training sets, and then exploits the Euclidean distance of each training sample to determine K nearest neighbors for the test sample. Its second phase represents the test sample as a linear combination of the determined K nearest neighbors and uses the representation result to perform classification. In addition, we use various numbers of DCT coefficients and DFT amplitude spectra to test the effect on our algorithms. The experimental results show that our method outperforms the two-phase face recognition method based on space domain of face images.     

Frequency-domain Hadamard spectroscopy

A new technique is proposed for multichannel excitation and detection of NMR signals in the frequency domain, an alternative to the widely used pulse-excited Fourier transform method. An extensive array of N radiofrequency irradiation channels covers the spectrum of interest. A selective radiofrequency pulse sequence is applied to each channel, generating a steady-state NMR response acquired one-point-at-a-time in the intervals between pulses. The excitation pattern is repeated N times, phase-encoded according to a Hadamard matrix, and the corresponding N composite responses are decoded by reference to the same matrix. This multiplex technique offers the same sensitivity advantage as conventional Fourier transform spectroscopy. The irradiation pattern may be tailored to concentrate on interesting spectral regions, to facilitate homonuclear double resonance, or to avoid exciting strong solvent peaks. As no free induction decay is involved, the new method avoids problems of pulse breakthrough or lineshape distortion by premature termination of the time-domain signal.     

Characterization of carbon nanotube filters and other carbonaceous materials by Raman spectroscopy—II: study on dispersion and disorder parameters

Recently, we have reported on the characterization of various carbonaceous materials including multiwalled carbon nanotube (MWCNT) filters, which have specific molecular filtering capabilities and good mechanical strength and can be produced in bulk as highly aligned arrays of bundles of CNTs. We have extended our studies using Fourier transform‐Raman spectroscopy with 1064 nm excitation wavelength and a rotating sample holder in the region 1000–2800 cm⁻¹, in addition to 532 and 785 nm, which were used for Raman excitation in our previous study. Raman spectra were analyzed for band positions and line shape with special emphasis on the D‐, G‐ and G′‐ bands. For the single‐walled species, Carbotrap and graphite spectra were also recorded with 488 nm excitation. A dispersion study has been made from the Raman data available with the different excitation wavelengths. Slight band shifts and band broadening could be observed under the two sample conditions, one with the stationary sample and the other with sample rotation. The spectral changes are related to the excessive heating caused in a stationary sample by laser irradiation. Based on our findings in this study combined with our earlier study, we can state that only a careful line shape analysis and study of intensity pattern of the D‐ and G‐Raman bands under well‐defined measurement conditions lends itself as a good measure of degree of alignment in the MWCNT bundles. Copyright © 2010 John Wiley & Sons, Ltd.     

阿达玛变换在核磁共振成象中的应用

阿达玛变换应用到核磁共振成象技术中,能提高成象技术的灵敏度。本文阐述了阿达玛变换在线扫描核磁共振成象中应用原理,推出了合成的激发信号相位与阿达玛编码关系。得到频率合成的激发信号相位表,据该表合成的激发信号产生多个自旋回波,能使核磁共振成象技术速度快、灵敏度高。文中还对该方法作了深入的讨论。     

基于高速公路裂纹局部线性特征内容的脊波变换域算法研究

利用频域中傅里叶变换投影定理,提出一种新的离散脊波实现算法,应用于高速公路局部线性裂纹的检测取得较好效果。详细阐述了离散脊波的实现步骤以及对标准图像进行脊波变换的模拟结果,并提出拉东(Radon)变换重建原图像的基本条件。上述定理应用于复杂背景下的路面检测,结合直方图均衡化算法消除背景噪声;选用基于样本估计的阈值方法对脊波分解的各层系数进行处理去除随机噪声。选用不同的重构系数进行计算,得到脊波变换后重构图像的信噪比优于二维小波变换(低频大于20dB)以及二维小波变换加魏纳滤波变换(平均大于3dB)。通过图像的二值化处理提取局部线性裂纹,其分辨力极限达到2mm精度。     

Reconstruction of band-limited signals from multichannel and periodic nonuniform samples in the linear canonical transform domain

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. This paper addresses the problem of signal reconstruction from multichannel and periodic nonuniform samples in the LCT domain. Firstly, the multichannel sampling theorem (MST) for band-limited signals with the LCT is proposed based on multichannel system equations, which is the generalization of the well-known sampling theorem for the LCT. We consider the problem of reconstructing the signal from its samples which are acquired using a multichannel sampling scheme. For this purpose, we propose two alternatives. The first scheme is based on the conventional Fourier series and inverse LCT operation. The second is based on the conventional Fourier series and inverse Fourier transform (FT) operation. Moreover, the classical Papoulis MST in FT domain is shown to be special case of the achieved results. Since the periodic nonuniformly sampled signal in the LCT has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived MST and the specific space-shifting property of the LCT. Last, the potential applications of the MST are presented to show the advantage of the theory.     

Applications of quantum Fourier transform in photon-added coherent state

Quantum Fourier transform is realized by the Hadamard gate in a quantum computer, which can also be considered as a Hadamard transform. We introduce the Hadamard transformed photon-added coherent state （HTPACS）, which is obtained by letting the photon-added coherent state （PACS） across the quantum Hadamard gate, from this result. It is found that the HTPACS can be considered as a coordinate-momentum mutual exchanging followed by a squeezing transform of the PACS. In addition, the non-classical statistical properties of HTPACS, such as squeezing coefficient, Mandel parameter, etc., are also discussed.     

Acoustic characteristics of a multichannel long line of the flexural type

The properties of an acoustic object represented by a multichannel long line of the flexural type are considered. Analytical formulas are obtained for the basic acoustic characteristics of a multichannel long line with an arbitrary number of flexurally oscillating single lines constituting it: the input impedance, the resonance frequencies, and the reflection and transmission coefficients are determined for an insulating multichannel long line, including the case of a cascade connection. Numerical calculations are performed and the plots are presented for the frequency dependences of the reflection and transmission coefficients for various parameters of the constituting lines. It is demonstrated that the acoustic characteristics of insulating multichannel long lines have certain advantages in comparison with the characteristics of similar objects based on single lines.     

Shape reconstruction from gradient data in an arbitrarily-shaped aperture by iterative discrete cosine transforms in Southwell configuration

The shape reconstruction from gradient data is a common problem in many slope-based metrology applications. In practice, the gradient data may not be ideally available for the whole field of view as expected, due to the aperture or the unmeasurable part of sample. An iterative method by using discrete cosine transforms is addressed in this work to deal with the integration problem with incomplete gradient dataset in Southwell configuration. Simulation indicates that the discrete cosine transform provides better initial values than discrete Fourier transform does, and it converges to a more accurate level by updating with spectrum-based slopes comparing to the slope updates from finite difference in classical method. Experimental results show the feasibility of the proposed approach in a practical measurement.     

A novel image encryption scheme based on Kepler's third law and random Hadamard transform

In this paper, a novel image encryption scheme based on Kepler's third law and random Hadamard transform is proposed to ensure the security of a digital image. First, a set of Kepler periodic sequences is generated to permutate image data, which is characteristic of the plain-image and the Kepler's third law. Then, a random Hadamard matrix is constructed by combining the standard Hadamard matrix with the hyper-Chen chaotic system, which is used to further scramble the image coefficients when the image is transformed through random Hadamard transform. In the end, the permuted image presents interweaving diffusion based on two special matrices, which are constructed by Kepler periodic sequence and chaos system. The experimental results and performance analysis show that the proposed encrypted scheme is highly sensitive to the plain-image and external keys, and has a high security and speed, which are very suitable for secure real-time communication of image data.     

基于Hadamard矩阵优化排序的快速单像素成像

为提升单像素成像速度,提出了基于Hadamard矩阵优化排序的压缩采样解决方案.利用数值仿真和室外实验对提出的5种排序方法进行了对比分析.研究结果表明:按Haar小波变换系数绝对值排序时单像素成像效果最优,排序对应到Walsh序后可利用快速变换重建图像,速度达300帧/秒@64×64像素;最优排序下,采样率25%仍可重建图像,采样速度可提升4倍.针对排序方法与成像信噪比关系,从关联成像角度给出了其物理解释:测量基矩阵元邻域数值相等的区域面积等效于光场二阶相干面积,当光场二阶相干面积随测量基由大到小排序时成像效果最优.本文研究成果可用于提升单像素成像速度,具有实用价值.     

One-dimensional lazy quantum walks and occupancy rate

In this paper, we discuss the properties of lazy quantum walks. Our analysis shows that the lazy quantum walks have O(t n) order of the n-th moment of the corresponding probability distribution, which is the same as that for normal quantum walks. The lazy quantum walk with a discrete Fourier transform(DFT) coin operator has a similar probability distribution concentrated interval to that of the normal Hadamard quantum walk. Most importantly, we introduce the concepts of occupancy number and occupancy rate to measure the extent to which the walk has a(relatively) high probability at every position in its range. We conclude that the lazy quantum walks have a higher occupancy rate than other walks such as normal quantum walks, classical walks, and lazy classical walks.     

基于小波阀值消噪的硝铵NQR信号处理

针对硝铵（AN）核电四极矩共振（NQR）信号通过傅立叶变换频域分析缺乏信号时域信息的特点,对硝铵NQR信号进行时频分析,达到从强背景噪声下检测出NQR信号的目的. 引入小波分析阀值去噪的方法对硝铵NQR信号进行处理. 对处理后数据与标准信号之间的相关系数进行分析. 实验结果表明小波阀值去噪方法可以成功检测到硝铵的NQR信号.     

Multiparty Quantum Secret Sharing Using Quantum Fourier Transform

A （n, n）-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform. In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert. Fhrthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant. Security analysis shows that our scheme is secure. Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.     

Blind source separation of multichannel electroencephalogram based on wavelet transform and ICA

Combination of the wavelet transform and independent component analysis （ICA） was employed for blind source separation （BSS） of multichannel electroencephalogram （EEG）. After denoising the original signals by discrete wavelet transform, high frequency components of some noises and artifacts were removed from the original signals. The denoised signals were reconstructed again for the purpose of ICA, such that the drawback that ICA cannot distinguish noises from source signals can be overcome effectively. The practical processing results showed that this method is an effective way to BSS of multichannel EEG. The method is actually a combination of wavelet transform with adaptive neural network, so it is also useful for BBS of other complex signals.     

Z变换在磁化等离子体电磁脉冲传播时域分析中的应用

 通过Z变换的方法,将与频率有关的磁化等离子体的介电常数由频域变换到Z域,推导了Z变换形式的时域有限差分法计算式,模拟了电磁脉冲在磁化等离子体中的传播。经过离散傅里叶变换,给出了电磁波通过磁化等离子体后的反射系数和透射系数与频率的关系。还给出了模拟结果和理论值的对比。结果表明,Z变换算法的模拟结果比卷积分更接近理论值。     

The multiple-parameter discrete fractional Hadamard transform

Discrete fractional Hadamard transform (DFrHaT) is a generalization of the Hadamard transform, which has been widely used in signal processing. In this paper, we present the multiple-parameter discrete fractional Hadamard transform (MPDFrHaT), which has multiple order parameters instead of only one in DFrHaT. The proposed MPDFrHaT is shown to possess all of the desired properties of DFrHaT. In fact, it will reduce to DFrHaT when all of its order parameters are the same. We also propose a novel encryption technique, double random amplitude (DRA) encoding scheme, by cascading twofold random amplitude filtering. As a primary application, we exploit the multiple-parameter feature of MPDFrHaT and double random amplitude encoding scheme for digital image encryption in the MPDFrHaT domain. Results show that this method can enhance data security.     

Gamma畸变的相位误差模型与Gamma标定技术

Gamma畸变是数字相移测量技术的主要误差源。以通用的均匀步长相移技术为对象,分析了Gamma畸变对相位计算的影响,建立了相位误差与谐波系数的关系模型,证明了各阶谐波系数在Gamma值影响下的递推公式,进而提出了基于离散傅里叶变换的Gamma标定技术。基于此Gamma标定值,通过Gamma预矫正降低相位误差。实验结果表明,标定的Gamma值在整个像平面具有较强的稳定性,Gamma矫正后使相位误差减小了77.5%,在曲面测量的结果中,水波纹明显得到抑制,曲面质量得以提高。     

Compression and reconstruction of MRI images using 2D DCT.

In magnetic resonance imaging (MRI), the original data are sampled in the spatial frequency domain. The sampled data thus constitute a set of discrete Fourier transform (DFT) coefficients. The image is usually reconstructed by taking inverse DFT. The image data may then be compressed using the discrete cosine transform (DCT). We present here a method of treating the data that combines two procedures, image reconstruction and data compression. This method may be particularly useful in medical picture archiving and communication systems (PACS) where both image reconstruction and compression are important issues.