Cosh-Hilbert变换反演的矩方法及其在单光子发射计算机断层成像中的应用

基于反演Hilbert变换的Tricomi公式和双曲余弦函数Taylor展开,给出一种反演双曲余弦Hilbert变换(CHT)的数值算法,并应用于单光子发射计算机断层成像.利用Taylor展开将函数的CHT变换表示为其Hilbert变换和由各阶矩组成的修正项.利用Tricomi公式得到一个关于函数各阶矩的线性方程组.通过对方程组的截断,可以求得函数的有限阶矩,并得到函数的近似重建.通过数值实验与精确重建公式进行比较,验证了算法的有效性.     

Study of the algorithm in the phase retrieval using the logarithmic Hilbert transform

The phase retrieval from a modulus of the scattered wave field at the Fourier transform plane of an object is considered in this paper by using the logarithmic Hilbert transform. When the phase is evaluated by using the logarithmic Hilbert transform from the modulus at the Fourier transform plane of the object with the direct component (for example, the phase object), the distortion appears in the reconstructed object obtained from an inverse Fourier transform of the complex wave consisting of the evaluated phase and the modulus. Here, the cause for the appearance of the distortion is made clear and a simple algorithm is presented to reduce the distortion of the reconstructed object.     

基于希尔伯特变换的干涉条纹相位解调新算法

提出了一种新的应用希尔伯特变换解调干涉条纹相位的算法,可以从单幅干涉条纹图中解调出全场相位分布.在实际应用中,常借助傅里叶变换实现希尔伯特变换算法,但是会忽略负频率成分,造成相位信息的丢失.对于相位分布非单调变化的干涉条纹,提出了一种判断函数,用来计算相位信息零频率点的分布.利用相位的零频率点分布构造了一个二元模板,使用该模板对本文提出的两次希尔伯特变换法产生的包裹相位图进行修正.对修正后的包裹相位图进行解包裹处理,可以得到连续的全场相位分布.对该方法用计算机模拟进行了验证.     

A numerical spatial carrier for single fringe pattern analysis algorithm

Hilbert transform and continuous wavelet transform are combined to form an algorithm for the analysis of a single fringe pattern with open or closed fringes. Only one recorded fringe pattern is needed to extract the phase information. A second π/2 phase shifted fringe pattern should first be generated from the other using Hilbert transform to superpose numerically the spatial carrier. Several phase extraction techniques are conceived to demodulate fringe patterns. In this paper, the wavelet technique is used to obtain the required phase distribution. The algorithm offers an advantage that it is appropriate when the spatial carrier is impossible to be added experimentally. Finally, a simulation was carried out to validate the algorithm, giving good results.     

Quantum Hilbert Image Scrambling

Analogies between quantum image processing (QIP) and classical one indicate that quantum image scrambling (QIS), as important as quantum Fourier transform (QFT), quantum wavelet transform (QWT) and etc., should be proposed to promote QIP. Image scrambling technology is commonly used to transform a meaningful image into a disordered image by permutating the pixels into new positions. Although image scrambling on classical computers has been widely studied, we know much less about QIS. In this paper, the Hilbert image scrambling algorithm, which is commonly used in classical image processing, is carried out in quantum computer by giving the scrambling quantum circuits. First, a modified recursive generation algorithm of Hilbert scanning matrix is given. Then based on the flexible representation of quantum images, the Hilbert scrambling quantum circuits, which are recursive and progressively layered, is proposed. Theoretical analysis indicates that the network complexity scales squarely with the size of the circuit’s input n.     

希尔伯特变换条纹分析法及其在非球面镜测量上的应用

提出了利用离散的希尔伯特变换法解调干涉条纹相位的方法,叙述了希尔伯特变换法解调相位的原理,并从单一的干涉图样中提取出条纹信号的正弦和余弦部分,正弦与余弦比值的反正切即为干涉相位;然后利用泽尼克多项式拟合,实现波前重建;最后讨论了条纹相位的算法,误差修正和测量面形的应用,从而实现对非球面镜的检测。实验表明,该方法可获得均方根(RMS)的精度为λ／10。     

相位恢复算法在量子关联衍射成像中的应用研究

随着研究工作的逐步深入,目前已经利用经典热光源实现了关联衍射成像,使得该技术有望在X射线以及中子衍射成像等方面得到广泛应用。在实验利用非相干光得到物体无透镜傅里叶变换频谱的基础上,采用误差消除与输入输出恢复算法,并结合过采样理论,实现了实验所用物体透射率函数的恢复。分别得到了纯振幅物体的振幅分布函数与纯相位物体的相位分布函数。此外,还讨论了实验所得傅里叶变换频谱的噪声等因素对图像恢复结果的影响。     

基于HHT与LSSVM的远区核爆电磁脉冲识别

为实现远区核爆电磁脉冲（NEMP）和闪电电磁脉冲（LEMP）的有效识别,提出一种基于希尔伯特黄变换（HHT）和最小二乘支持向量机（LSSVM）的识别算法。采用希尔伯特黄变换对远区NEMP和LEMP进行分析,利用两种信号的Hilbert谱在不同频带上分布的差异性,选择谱图中两个区域的能量占比作为信号的特征,选择LSSVM作为分类器进行分类识别。实验结果表明,采用能量占比特征可有效识别NEMP和LEMP,且综合识别率可达到98.59%。     

基于Hilbert变换实现数字全息高精度相位重建

为了提高数字全息相位重建精度,研究了基于Hilbert变换重建相位的理论和方法,并通过像面数字全息实验对该方法的有效性进行了验证,同时与数字全息常规重建方法得到的结果进行了比较.结果表明:Hilbert变换本身具有消除直流项的作用,对利用频域滤波滤除零级谱后的全息图进行Hilbert变换,能够彻底消除零级衍射项的干扰,从而提高相位重建精度.与常规重建结果相比,基于Hilbert变换的相位重建结果的标准偏差降低了14.0%.本文结果对提高数字全息相位重建精度具有重要的指导意义.     

Microwave radiation generated by a high-power air explosion

The special features of the generation of microwave radiation by a high-power air explosion accompanied by ionizing radiation are discussed. Coherent pulse caused by asymmetry of the ejection of gamma quanta from a source, incoherent bremsstrahlung of a partially ionized plasma, incoherent radiation of the shock wave front, and radiation in spectral lines lying inside air transparency windows are considered.     

单通道光学相关实现击中与否运算

给出了一种单通道光学相关实现击中与否运算的算法和光学装置，此法基于形态学中的腐蚀运算和光学相关的关系及阈值操作，在非相干光学相关器中，将前景结构核元素编码为１，背景结构核元素编码为ａ（ａ满足一定条件），只需用原图像与前景和背景结构进行相关，然后对相关结果取阈值的Ｋ（前景结构核元素的像素数）即可得到击中与否运算，击中与否运算可以光学并行一步实现。     

动态干涉条纹相位提取的抗干扰算法

为减小在动态干涉条纹的相位提取中噪声带来的计数误差,研究了在希尔伯特变换相位提取的基础上,利用反正切相位跳变特性,通过软件实现可逆计数的抗干扰算法。通过模拟实验对算法的抗干扰性能进行了验证,实验结果表明：所提出的相位提取算法具有较强的抗干扰性能,在信噪比为11时,算法仍然能得到正确的结果。     

辐射在相对论等离子体中非相干散射的结构因子

等离子体中粒子关联效应使辐射在等离子体内非相干散射的总截面等于汤姆逊截面乘上结构因子。本文给出辐射在相对论等离子体中非相干散射的结构因子。     

Speech enhancement method based on low-rank approximation in a reproducing kernel Hilbert space

Speech signal is corrupted unavoidably by noisy environment in subway, factory, and restaurant or speech from other speakers in speech communication. Speech enhancement methods have been widely studied to minimize noise influence in different linear transform domain, such as discrete Fourier transform domain, Karhunen-Loeve transform domain or discrete cosine transform domain. Kernel method as a nonlinear transform has received a lot of interest recently and is commonly used in many applications including audio signal processing. However this kind of method typically suffers from the computational complexity. In this paper, we propose a speech enhancement algorithm using low-rank approximation in a reproducing kernel Hilbert space to reduce storage space and running time with very little performance loss in the enhanced speech. We also analyze the root mean squared error bound between the enhanced vectors obtained by the approximation kernel matrix and the full kernel matrix. Simulations show that the proposed method can improve the computation speed of the algorithm with the approximate performance compared with that of the full kernel matrix.     

Experimental reconstruction of a long-period grating from its core-to-core transmission spectrum

We demonstrate, for the first time to our knowledge, reconstruction of the structure of a long-period grating from its measured core-to-core transmission spectrum intensity. The reconstruction is obtained by writing an auxiliary grating in cascade to the interrogated grating. Our reconstruction technique is based on using the Hilbert transform and a phase-retrieval algorithm. Using our method, we have reconstructed the structure of a uniform long-period grating with a 47% coupling efficiency.     

Modified Hilbert Curve for Rectangles and Cuboids and Its Application in Entropy Coding for Image and Video Compression

In our previous work, by combining the Hilbert scan with the symbol grouping method, efficient run-length-based entropy coding was developed, and high-efficiency image compression algorithms based on the entropy coding were obtained. However, the 2-D Hilbert curves, which are a critical part of the above-mentioned entropy coding, are defined on squares with the side length being the powers of 2, i.e., 2ⁿ, while a subband is normally a rectangle of arbitrary sizes. It is not straightforward to modify the Hilbert curve from squares of side lengths of 2ⁿ to an arbitrary rectangle. In this short article, we provide the details of constructing the modified 2-D Hilbert curve of arbitrary rectangle sizes. Furthermore, we extend the method from a 2-D rectangle to a 3-D cuboid. The 3-D modified Hilbert curves are used in a novel 3-D transform video compression algorithm that employs the run-length-based entropy coding. Additionally, the modified 2-D and 3-D Hilbert curves introduced in this short article could be useful for some unknown applications in the future.     

水下复杂壳体结构在多源激励下的振动及声辐射特性研究

为了综合评估水下复杂壳体结构在多源激励下的振动与声辐射特性,专门设计了一个多舱段复杂壳体模型,分别进行了单台设备激励、多台设备激励的壳体振动与声辐射试验。试验结果表明,多源激励下的结构响应和辐射声场可以近似为单源激励下结构响应和辐射声场的非相干叠加。通过对激励源与结构响应、辐射声场之间传递关系的理论分析,讨论了以单源激励响应非相干叠加合成得到多源激励响应的合理性和误差。研究结果对复杂壳体结构在实际激励下的振动与噪声预报具有重要价值。      

IKNO,a user facility for coherent terahertz and UV synchrotron radiation

IKNO (Innovation and KNOwledge) is a proposal for a multi‐user facility based on an electron storage ring optimized for the generation of coherent synchrotron radiation (CSR) in the terahertz frequency range, and of broadband incoherent synchrotron radiation ranging from the IR to the VUV. IKNO can be operated in an ultra‐stable CSR mode with photon flux in the terahertz frequency region up to nine orders of magnitude higher than in existing third‐generation light sources. Simultaneously to the CSR operation, broadband incoherent synchrotron radiation up to VUV frequencies is available at the beamline ports. The main characteristics of the IKNO storage and its performance in terms of CSR and incoherent synchrotron radiation are described in this paper. The proposed location for the infrastructure facility is Sardinia, Italy.     

Identification of nonlinear multi-degree-of freedom structures based on Hilbert transformation

The modeling method and identified method adapted to multi-degree-of-freedom structures with strucrural nonlinearities are established. The component mode synthesis method is used to establish the nonlinear governing equations by extending the connected relationships. Based on the modeling method, the Hilbert transform method is applied to identify the nonlinear stiffness of multi-degree-of-freedom structures. Nonlinear analysis and identification of a typical folding wing configuration with three freeplay hinges are investigated. The nonlinear governing equation is established based on present methods and the computing results of different stiffness are checked by finite element programming. In order to illustrate the influence of the nonlinearities, the frequency response characteristics of the structure are analyzed and Hilbert transform is performed. The Hilbert transform identification method is utilized to identify the nonlinear stiffness of nonlinear hinges in the time domain and several parametric studies are performed. In addition, the comparison of response is made to illustrate the feasibility of the methods. The results show that the extending component mode synthesis method in the present work can be used to establish the governing equation with structural nonlinearities. Based on the modeling method, the Hilbert transform identified method can be extended to multi-degree-of-freedom structures accurately.     

On the van Cittert-Zernike theorem

The van Cittert-Zernike theorem states that the spatial coherence over a space illuminated by an incoherent extended source is described by the Fourier transform of the intensity distribution over the source. The theorem is usually used in a restricted case of the spatial coherence in a plane parallel to the source plane and illuminated by an incoherent extended source of uniform intensity distribution. In this paper we re-examine the van Cittert-Zernike theorem by reviewing it in an original formulation and extend the theorem to the spatial coherence at any two points of a light field illuminated by an incoherent extended source having a non-uniform intensity distribution.