Compressed sensing MR image reconstruction using a motion-compensated reference

Compressed sensing (CS)-based methods have been proposed for image reconstruction from undersampled magnetic resonance data. Recently, CS-based schemes using reference images have also been proposed to further reduce the sampling requirement. In this study, we propose a new reference-constrained CS reconstruction method that accounts for the misalignment between the reference and the target image to be reconstructed. The proposed method uses a new image model that represents the target image as a linear combination of a motion-dependent reference image and a sparse difference image. We then use an efficient iterative algorithm to jointly estimate the motion parameters and the difference image from sparsely sampled data. Simulation results from a numerical phantom data set and an in vivo data set show that the proposed method can accurately compensate the motion effects between the reference and the target images and improve reconstruction quality. The proposed method should prove useful for several applications such as interventional imaging, longitudinal imaging studies and dynamic contrast-enhanced imaging.     

Limitation of carrier fringe methods in digital photoelasticity

The carrier fringes method has been proposed in digital photoelasticity in combination with techniques such as Fourier transform and phase shifting method, without considering the influence of the isoclinics on the isochromatic patterns analysis. Unlike other optical methods as moiré and holographic interferometry, in photoelasticity the light intensity emerging from a circular polariscope is related to both the isochromatic retardation and the isoclinic parameter. As it is shown by the theoretical analysis, owing to the misalignment between the principal stresses in the model and in the carrier, the computed retardation is affected by an error which is the same for all photoelastic methods based on the use of carrier fringes. Consequently, the photoelastic analysis carried out by methods that use carrier fringes cannot be applied as a full-field technique. In detail, numerical simulations show that the retardation error is comparable (less than 0.05 fringe orders) with that of other photoelastic methods provided that the misalignment between the principal stresses in the model and in the carrier is less than 30°. On the contrary, in the model zones where the misalignment is higher than 30°, the retardation measurement can be affected by non negligible errors (up to 0.25 fringe orders).     

Study of a misaligned flexibly coupled shaft system having nonlinear bearings and cyclic coupling stiffness—Theoretical model and analysis

A model which enables dynamic analysis of flexibly coupled misaligned shafts is presented. The model is setup to account for both angular and parallel misalignment in the presence of mass unbalance and incorporates a coupling having angular, torsional and axial flexibility. Among the important features is the ability to simulate both nonlinear bearing stiffness and coupling angular-stiffness anisotropy. The equations of motion are derived for the linear system, extended to include nonlinear bearing effects and subsequently transformed into non-dimensional form for general application. A series of numerical analyses are performed and the influence of important system parameters assessed thereby providing insight to the resulting static and dynamic forces and motions. Angular and parallel misalignments are shown to produce fundamentally different system response. It is found that the static preload induced by both types of misalignment can play a key role in producing complex vibration resulting from it's interaction with rotating-element anisotropy and bearing nonlinear properties. Bearing static forces are altered and rotating elements are subjected to alternating forces which could affect fatigue life. Bearing forces can be further modified by the application of transmitted torque. The potential for great variability in system response is shown to exist due to the participation of numerous influential variables.     

Damping lateral vibrations in rotary machinery using motor speed modulation

This paper outlines a new principle for damping lateral vibrations of rotary systems. According to this principle, no changes in the visco-elastic properties of the system to be damped are required. The method is based on the generation of a harmonic additive to the constant speed of rotation that provides significant damping of lateral vibrations at critical speeds of rotation. This concept is validated analytically using the method of averaging and additionally with the help of direct numerical integration. The solution is shown to represent Fourier series containing Bessel functions. Consequently, proper choice of the parameters of the additional harmonic component ensuring that the Bessel functions have minimum values results from a minimization of the solution itself. Thus, the analytical solution and numerical results prove this concept by showing an essential decrease of the amplitudes of lateral vibrations of the damped system compared with those of the undamped system. The physical explanation of this effect is presented.     

Investigation of Lamb elastic waves in anisotropic multilayered composites applying the Green’s matrix

This article presents a numerical study of dispersion characteristics of some symmetric and antisymmetric composites modelled as multilayered packets of layers with arbitrary anisotropy of each layer. The authors introduce a subsidiary boundary problem of three-dimensional elasticity theory for the system of partial differential equations describing the harmonic oscillations of the composite caused by a surface load. The problem reduces to a boundary problem for ordinary differential equations by employing the Fourier transform. An algorithm of constructing the Fourier transform of the Green’s matrix of the given boundary problem is presented. The wave numbers of Lamb waves propagating in composites, their phase velocity surfaces and group wave surfaces are presented through the poles of the transform of the Green’s matrix. The authors obtain the dispersion curves for different directions and frequencies and investigate the dispersion curves and surfaces of wave numbers, phase velocities and group wave surfaces for various composites. The numerical results are then compared with the results obtained by applying other methods.     

Optimizing the performance of single-mode laser diode system using genetic algorithm

In this correspondence, micro-genetic algorithm (MGA) application results for optimizing the performance of electronic feedback of a laser diode are presented. The goal of optimization is to find the maximum bandwidth of the laser diode with electronic feedback used in fiber optic digital communication. A numerical analysis of the system theory of the single-mode laser diode to obtain numerical results of the gain, the pulse response, and the harmonic distortion for electronic feedback is also presented. The dependence of the system gain on the feedback gain and delay is examined. The pulse response is studied and it is shown that a transmission rate over 1 Gbyte/s can be achieved.     

失调单球面折射系统的衍射积分和分数傅里叶变换

根据球面的几何特征，分析了单球面折射光学系统折射面倾斜和偏心时的失调特征；由失调元件矩阵和共轴元件矩阵的依次相乘，得到了完备的描述失调单球面折射光学系统的矩阵；从系统衍射积分与失调矩阵元的关系导出了该系统的失调衍射积分，并利用单球面折射光学系统的分数傅里叶变换结构参数得到了系统失调时的分数傅里叶变换结果.这些结果可用于数值计算和模拟该系统失调时对输入复振幅的衍射和分数傅里叶变换.     

Vibration response of misaligned rotors

Misalignment is one of the common faults observed in rotors. Effect of misalignment on vibration response of coupled rotors is investigated in the present study. The coupled rotor system is modelled using Timoshenko beam elements with all six dof. An experimental approach is proposed for the first time for determination of magnitude and harmonic nature of the misalignment excitation. Misalignment effect at coupling location of rotor FE model is simulated using nodal force vector. The force vector is found using misalignment coupling stiffness matrix, derived from experimental data and applied misalignment between the two rotors. Steady-state vibration response is studied for sub-critical speeds. Effect of the types of misalignment (parallel and angular) on the vibration behaviour of the coupled rotor is examined. Along with lateral vibrations, axial and torsional vibrations are also investigated and nature of the vibration response is also examined. It has been found that the misalignment couples vibrations in bending, longitudinal and torsional modes. Some diagnostic features in the fast Fourier transform (FFT) of torsional and longitudinal response related to parallel and angular misalignment have been revealed. Full spectra and orbit plots are effectively used to reveal the unique nature of misalignment fault leading to reliable misalignment diagnostic information, not clearly brought out by earlier studies.     

Error-compensating algorithms in phase-shifting interferometry: a comparison by error analysis

In this paper, two families of phase-shifting algorithms with π/2 phase steps are studied. In family I, three new algorithms are derived by using the averaging technique based on the Surrel six-sample algorithm with phase shifts of π/2. Family II includes four well-known algorithms derived by the averaging technique based on the conventional four-sample algorithm with π/2 phase steps. A polynomial model of phase-shift errors used to describe general expressions for calculation of the correct object phase via the Fourier spectra analysing method as a function of the harmonic order in the fringe signal is presented. The error-compensating properties of the algorithms in families I and II are investigated by the Fourier spectra analysing method. It is found that the averaging technique, when used in any of the algorithm with π/2 phase steps, can improve the phase-shifting algorithm property: it is insensitive to phase-shift error when the fringe signal contains the first harmonic, but it can't be used to enhance the phase-shifting algorithm properties when the fringe signal contains higher order harmonics (n2). P–V (peak–valley) phase errors are calculated by the computer simulation and tables and plots are presented, from which the algorithms in families I and II are compared. It is shown that the algorithms in family I are more insensitive to phase-shift errors when the fringe signal contains the second harmonic and the algorithms in family II are more insensitive to phase-shift errors when the fringe signal is a sinusoidal waveform.     

总变差约束的数据分离最小图像重建模型及其Chambolle-Pock求解算法

基于优化的迭代法,可以结合压缩感知和低秩矩阵等稀疏优化技术高精度地重建图像.其中,总变差最小（total variation minimization,TV）模型是一种简单有效的优化模型.传统的约束TV模型,使用数据保真项为约束项,TV正则项为目标函数.本文研究TV约束的、数据分离最小（TV constrained,data divergence minimization,TVcDM）新型TV模型及其求解算法.详细推导了TVcDM模型的Chambolle-Pock（CP）算法,验证了模型及算法的正确性;分析了算法的收敛行为;评估了模型的稀疏重建能力;分析了模型参数的选择对重建的影响及算法参数对收敛速率的影响.研究表明,TVcDM模型有高精度稀疏重建能力;TVcDM-CP算法确保收敛,但迭代过程中有振荡现象;TV限对重建有重要影响,参数值过大会引入噪声而过小会模糊图像细节;算法参数的不同选取会导致不同的收敛速率.     

Effect of laser source nonlinearity on optical heterodyne interferometry

In this paper, an optical heterodyne interferometric detection model with a frequency-ramped laser diode (LD) has been analyzed. The effect of the nonlinearity of the LD source on the optical heterodyne interferometry has been investigated in two different ways, which are the power-distortion Fourier series analysis and the harmonic distortion analysis. The general formulation between the tangent of the tested phase and the interference fringe have been presented with the analysis of the beat signal in the frequency domain by each methodology. The numerical results of these formulations have been presented.     

Phase Recovery from the Raman Excitation Profile,Time Domain Information and Transform Theory

The phase recovery from the vibrational Raman excitation profile (REP), which contains only the modulus of the Raman amplitude, is discussed for the general situation where the Raman amplitude, with excitation energy extended in the complex plane, may have zeros in the right-half plane. The focus is on the dispersion method, with all results derived by contour integration. The new results for phase recovery, however, apply to both the dispersion and maximum entropy methods. An iterative procedure, with rapid convergence, is presented to overcome the experimental REP data being given in a limited energy range. The forward transform from the electronic absorption spectrum (ABS) to the REP and the inverse transform from the REP to the ABS are presented in a unified manner. The ubiquitous Hilbert transform is shown to be readily evaluated by the fast Fourier transform algorithm. Calculations are presented for β-carotene, a two-mode harmonic model with diffuse vibrational structure, azulene and iodobenzene to illustrate the theory. © 1997 John Wiley & Sons, Ltd.     

基于双谱的谐波信号重构

提出了一种基于双谱分析的谐波信号精确重构方法.该方法通过在被测信号中加入一相位为0幅值为1的半基频信号,并对该合成信号进行双谱分析,实现了被测信号相位和幅值的精确求解,解决了已有基于双谱的信号重构方法中所存在的相对相移问题.仿真结果验证了该方法的有效性.     

Chord length distributions in binary stochastic media in two and three dimensions

Simple models for transport through stochastic media usually assume that the chord lengths of materials are distributed exponentially. Theory predicts that, in a medium consisting of disks/spheres that can interpenetrate, chord lengths in the background material (between the disks/spheres) should exactly follow an exponential. In a medium with impenetrable (non-overlapping) disks/spheres, the distribution is only approximately exponential. This paper demonstrates, through direct numerical simulations, that for randomly distributed disks in 2D and spheres in 3D, with distributions of radii, chord lengths in the background material (between the disks/spheres) are accurately described by exponentials over five orders of magnitude when the material is dilute. The chord lengths inside the disks and spheres are not exponentially distributed, but those distributions can be calculated. A scaling relationship between the mean chord lengths in the two materials is presented for an infinite medium. By knowing the mean properties of the disks/spheres in a medium, this relationship allows one to accurately describe the statistical properties of the background material. The stochastic simulations are validated by this infinite medium relationship. When the fraction of space occupied by the disks or spheres becomes large, the distributions are no longer accurately described by an exponential.     

DYNAMIC RESPONSE OF TWO ROTORS CONNECTED BY RIGID MECHANICAL COUPLING WITH PARALLEL MISALIGNMENT

The effect of parallel misalignment on the lateral and torsional responses of two rotating shafts (Jeffcott rotors) is examined with theoretical and numerical analysis. The general equations of motion are derived and given in dimensionless form to represent the general case. The equations of motion revealed that parallel misalignment couples the translation and angular deflections through the stiffness matrix and the force vector. The non-linear equations are solved numerically using a combination of Newmark and Newton-Raphson methods to determine the dimensionless frequency and transient responses in terms of misalignment magnitude. The numerical results show that the system natural frequencies are excited at transient condition due to the presence of pure parallel misalignment. At steady state condition, the 1×-rotational speed excitation is present in the translation and angular directions, which indicates that parallel misalignment can be a source of both torsional and lateral excitations.     

Fast implementation of sparse iterative covariance-based estimation for source localization

Fast implementations of the sparse iterative covariance-based estimation (SPICE) algorithm are presented for source localization with a uniform linear array (ULA). SPICE is a robust, user parameter-free, high-resolution, iterative, and globally convergent estimation algorithm for array processing. SPICE offers superior resolution and lower sidelobe levels for source localization compared to the conventional delay-and-sum beamforming method; however, a traditional SPICE implementation has a higher computational complexity (which is exacerbated in higher dimensional data). It is shown that the computational complexity of the SPICE algorithm can be mitigated by exploiting the Toeplitz structure of the array output covariance matrix using Gohberg-Semencul factorization. The SPICE algorithm is also extended to the acoustic vector-sensor ULA scenario with a specific nonuniform white noise assumption, and the fast implementation is developed based on the block Toeplitz properties of the array output covariance matrix. Finally, numerical simulations illustrate the computational gains of the proposed methods.     

一种有效解决离轴数字全息相图倾斜畸变的数字参考平面方法

离轴数字全息中使用倾斜的平面参考波以消除成像中的零级衍射和共轭像是一种简捷和常用的方法,然而该方法遇到的一个困扰是,由于倾斜参考波引入了附加的载波频率并很难通过实验测量准确地获得附加的载波频率值或倾角,因此会导致重建的相图出现一定的倾斜畸变而无法完全修正.本文提出了一种数字参考平面算法以解决这一问题.该算法利用重建相图的平坦区域选点构建一个能准确表征相图倾斜的数字参考平面,并建立该平面参量与参考波载波频率的数学关系和作为随后相图畸变修正迭代计算的判据.该算法简单有效,不仅能实现对倾斜相位畸变的准确修正,而且能准确地获得倾斜平面参考波的附加载波频率.由于在相位解包裹重建中结合了抑噪处理,因此该方法在环境和系统噪声的影响下仍然有效,实验结果验证了理论设计的有效性.     

块稀疏水声信道的改进压缩感知估计

压缩感知信道估计可利用信道稀疏特性提高估计性能,但对于具有典型块稀疏分布的水声信道,经典的l₀或l₁范数无法很好地描述块稀疏特性。利用水声信道块稀疏分布规律特性提出一种能够识别块稀疏结构的块稀疏似零范数,并在稀疏恢复信道估计算法中引入块稀疏似零范数约束项,进一步推导了复数域块稀疏似零范数恢复迭代算法,该算法通过对块稀疏似零范数进行梯度下降迭代并将梯度解投影至解空间来获得水声信道的块稀疏似零范数估计。数值仿真和海上水声通信实验结果表明该算法相对经典的稀疏信道估计算法有较明显的性能改善。通过算法推导、仿真和实验可获取结论:利用水声信道的块稀疏特性进行压缩感知重构可有效提高信道估计性能。     

适用于圆筒形增益区的同轴四镜腔的失调分析

采用矩阵光学方法,对适用于可见光的圆筒形增益区同轴四镜腔中的腔镜因倾斜而产生的失调特性进行了分析,给出了相关计算公式。该四镜腔由同轴的一个复曲面全反镜和两个光学玻璃加工的透镜和一个平面输出镜组成。以He-Ne激光器为例,给出了数值计算结果,关键元件复曲面镜的失调对输出的影响较大。这为腔元件的加工以及腔镜的安装调试提供了参考。     

Numerical methods for solving one-dimensional cochlear models in the time domain

In this article, a robust numerical solution method for one-dimensional (1-D) cochlear models in the time domain is presented. The method has been designed particularly for models with a cochlear partition having nonlinear and active mechanical properties. The model equations are discretized with respect to the spatial variable by means of the principle of Galerkin to yield a system of ordinary differential equations in the time variable. To solve this system, several numerical integration methods concerning stability and computational performance are compared. The selected algorithm is based on a variable step size fourth-order Runge-Kutta scheme; it is shown to be both more stable and much more efficient than previously published numerical solution techniques.