New fourth-order partial differential equations for filtering in electronic speckle pattern interferometry fringes

Partial differential equations (PDEs) based methods have been demonstrated to be a powerful tool for filtering in electronic speckle pattern interferometry fringe or wrapped phase patterns. In this paper, we derive the new fourth-order partial differential equations (NFOPDE) with a better performance for filtering in electronic speckle pattern interferometry fringe patterns based on the variational methods. We test the proposed models on two computer-simulated speckle fringe patterns and an experimentally obtained fringe pattern, respectively, and compare our models with the widely used, well-known the second-order selective degenerate diffusion PDE model (SOSDPDE) and the published fourth-order PDE model (PFOPDE). The proposed NFOPDE can overcome the shortages that both the SOSDPDE and PFOPDE encounter. In all cases, our NFOPDE outperforms SOSDPDE and PFOPDE.     

Anisotropic partial differential equation noise-reduction algorithm based on fringe feature for ESPI

Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a new anisotropic partial differential equation noise-reduction algorithm based on fringe orientation for interferometric fringe patterns. The proposed equation performs diffusion along the two directions of fringe gradient and isophote line, which are extracted accurately according to fringe feature. By restriction of diffusion in the gradient direction of fringe patterns, this method can provide optimal results in denoising but does not destroy fringe edges. The experimental results show that this technique is more capable of significantly improving the quality of the fringe patterns than the classical anisotropic diffusion equation proposed by Perona and Malik. Based on our filtered fringe patterns, the phase map obtained by phase-shifting technique can be extracted more accurately. It is an effective pre-processing method for electronic speckle pattern interferometry.     

Homomorphic partial differential equation filtering method for electronic speckle pattern interferometry fringes based on fringe density

Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a homomorphic partial differential equation filtering method for interferometry fringe patterns. The diffusion speed of the equation is determined based on the fringe density. We test the new method on the computer-simulated fringe pattern and experimentally obtain the fringe pattern, and evaluate its filtering performance. The qualitative and quantitative analysis shows that this technique can filter off the additive and multiplicative noise of the fringe patterns effectively, and avoid blurring high-density fringe. It is more capable of improving the quality of fringe patterns than the classical filtering methods.     

基于Gabor滤波的散斑条纹图平滑方法

提出了一种基于伽博(Gabor)滤波的散斑条纹图平滑方法.通过加窗傅里叶运算提取散斑条纹图的条纹频率和条纹梯度方向,并利用它们确定具有频率和方向选择性的Gabor滤波器对散斑条纹图进行Gabor滤波.数值模拟和实验结果表明,该方法在滤除散斑噪声的同时能够有效的保留散斑条纹图的条纹结构,为从单幅散斑条纹图中进一步提取条纹相位场奠定了良好的基础.     

基于小波变换条纹修补和条纹自相似性的干涉条纹极值提取

提出了基于小波变换的条纹修补方法和利用干涉条纹自相似性的条纹灰度极值自动判读方法.基于小波变换的条纹修补方法包括滤除噪音、多尺度小波变换、模极大值检测滤除奇异区域、近似信号自动修补,在此基础上进行多项式拟合,首先实现最外层条纹灰度极值的自动提取.基于干涉条纹自相似性的条纹灰度极值自动判读方法是通过逐渐平移拟合区域,准确地提取了内层条纹的灰度极值位置,从而可以处理整幅图片的干涉条纹.此方法的特点是自适应、无需人为设定参量、处理速度快.实验结果表明,该方法有很好的可靠性和准确性,并且处理区域大、用时少,仅需对图片扫描一次即可提取全部条纹的灰度极值.     

基于调制方向提取载波散斑条纹中心线的方法

条纹中心线法是一种重要的电子散斑干涉条纹解调方法,其前提条件是获得高准确度的条纹中心线.本文在分析载波电子散斑干涉条纹自身特征的基础上,提出了一种基于载波条纹调制方向提取条纹中心线的方法.该方法首先通过同态滤波有效滤除高频乘性散斑噪音,提取出载波条纹;然后应用基于调制方向提取中心线算法确定载波条纹灰度极值点并做二值化处理;再采用基于中心线拟合或者基于条纹间距的边沿中心线补偿法,获得完整的条纹中心线图.实验结果表明:该方法简单、可靠,能快速、准确地提取出连续的中心线.     

散斑干涉相位条纹图的频域滤波处理

为了解决在数字散斑干涉技术测量时,散斑干涉相位条纹图像中大量噪声对相位解包裹结果和精度产生严重影响的问题,介绍了一种条纹正余弦分解和频域低通滤波结合的方法,实现了散斑干涉相位条纹图的高精度滤波。该方法的基本思路是在对相位图像进行滤波处理前,先将相位图通过正余弦函数进行映射转换成两幅图,分别经过频域滤波,然后再合成为相位图。这种分解频域滤波方法可以在滤波的同时,有效保留相位跳变信息。实验结果表明：与传统的图像降噪方法相比,该方法能够在保留图像“尖峰”信息的基础上,较好地滤除图像中的散斑噪声,方法简单有效,有效解决了传统滤波方法应用在相位条纹图中,相图灰度信息丢失10%~40%的问题。     

基于调制方向提取载波散斑条纹中心线的方法

条纹中心线法是一种重要的电子散斑干涉条纹解调方法,其前提条件是获得高准确度的条纹中心线.本文在分析载波电子散斑干涉条纹自身特征的基础上,提出了一种基于载波条纹调制方向提取条纹中心线的方法.该方法首先通过同态滤波有效滤除高频乘性散斑噪音,提取出载波条纹;然后应用基于调制方向提取中心线算法确定载波条纹灰度极值点并做二值化处理;再采用基于中心线拟合或者基于条纹间距的边沿中心线补偿法,获得完整的条纹中心线图.实验结果表明:该方法简单、可靠,能快速、准确地提取出连续的中心线.     

Hole-burning diffusion measurements in high magnetic field gradients

We describe methods for the measurement of translational diffusion in very large static magnetic field gradients by NMR. The techniques use a "hole-burning" sequence that, with the use of fringe field gradients of 42 T/m, can image diffusion along one dimension on a submicron scale. Two varieties of this method are demonstrated, including a particularly efficient mode called the "hole-comb," in which multiple diffusion times comprising an entire diffusive evolution can be measured within the span of a single detected slice. The advantages and disadvantages of these methods are discussed, as well as their potential for addressing non-Fickian diffusion, diffusion in restricted media, and spatially inhomogeneous diffusion.     

Semi-Lagrangian multistep exponential integrators for index 2 differential–algebraic systems

Implicit-explicit (IMEX) multistep methods are very useful for the time discretization of convection diffusion PDE problems such as the Burgers equations and the incompressible Navier–Stokes equations. In the latter as well as in PDE models of plasma physics and of electromechanical systems, semi-discretization in space gives rise to differential–algebraic (DAE) system of equations often of index higher than 1. In this paper we propose a new class of exponential integrators for index 2 DAEs arising from the semi-discretization of PDEs with a dominating and typically nonlinear convection term. This class of problems includes the incompressible Navier–Stokes equations. The integration methods are based on the backward differentiation formulae (BDF) and they can be applied without modifications in the semi-Lagrangian integration of convection diffusion problems. The approach gives improved performance at low viscosity regimes.     

基于双树复小波与波原子的图像扩散滤波

图像的非线性扩散滤波来源于热方程的思想,其关键在于计算适当的扩散系数和控制扩散方向. 在已有的扩散模型中,由于扩散系数仅依赖于图像的梯度,因而这类模型容易受噪声的干扰;同时,图像的细节信息(如纹理)容易被误认为是噪声而被去除. 为克服这些不足,首先给出了一种采用双树复小波变换计算扩散系数的方法;然后设计了一种用于图像滤波的非线性扩散模型,最后提出了基于双树复小波变换和波原子阈值相结合的图像滤波算法. 仿真结果表明,所提出的算法在对含噪图像滤波的同时,能够较好地保持图像的边缘和纹理等细节信息. 关键词： 图像扩散滤波 非线性扩散 波原子 双树复小波变换     

数字散斑条纹图的滤波方法

在现代数字散斑测量方法中，一般采用减模式来产生数字散斑条纹图，它是进一步图像处理的信息载体，同时不可避免地附带有大量的乘性噪声。为了保证测量精度，在进一步图像处理前必须对其进行降噪，选择合适的滤波方法显得尤为重要。在多年实际经验及阅读了大量文献的基础上，该文对国内外常用的数字散斑干涉条纹图滤波方法进行了分类阐述，选择了一些有代表性的方法予以实现，给出实验结果，并进行了对比分析。最后对数字散斑干涉条纹图滤波方法的发展方向给出了自己的看法。     

Time evolution of diffusion fringes in the Christiansen effect

When laser radiation is allowed to fall at the diffusion region separating two liquids in a Christiansen filter, a new fringe pattern appears. We termed it as “diffusion fringes”. In the present work, we have studied this interference fringe pattern and its time evolution. It has been observed that there is a definite co-relation between the shape of the fringe pattern and the width of the diffusion region. The time evolution of this fringe patterns indicates that as diffusion region increases the circular fringe becomes elliptical and finally straight. It is believed that a detailed investigation of these diffusion fringes will throw much needed light not only on the theory of the Christiansen effect but also on the rate of diffusion between two molecules.     

散斑条纹图的自适应窗口滤波方法

针对散斑噪声很难用常用的滤波方法进行滤除,在已有等值线滤波方法的基础上,提出一种更优的自适应窗口滤波方法。由于等值线窗口是在条纹方向图的基础上得到的,深入研究条纹方向的求取方法,提出了一种更为可靠的条纹方向求取算法,在得到高精度条纹方向的同时,还能估计出条纹的密度。使用等值线窗口技术,保持了窗口形状的自适应能力,然后利用对条纹密度的估计,根据条纹的宽度来确定滤波窗口的大小,实现了滤波窗口大小的自适应。最后,根据条纹方向和滤波后的图像可以直接得到条纹密度变化较大的单幅散斑图的相位结果。     

基于非线性偏微分方程的灰度图像骨架线提取方法

基于变分法提出用于计算灰度图像梯度矢量场的非线性偏微分控制方程,利用图像梯度矢量场的拓扑性,可实现骨架线的提取。该方法的主要优点是它的简单性,可直接应用于灰度图像,不需要任何的分割处理。把提出的方法应用于牛顿环干涉条纹中,并与广泛使用的分块二值化细化算法和极值跟踪法进行了比较,实验结果表明了本方法的良好性能。     

A general strategy for anisotropic diffusion in MR image denoising and enhancement

Anisotropic diffusion (AD) has proven to be very effective in the denoising of magnetic resonance (MR) images. The result of AD filtering is highly dependent on several parameters, especially the conductance parameter. However, there is no automatic method to select the optimal parameter values. This paper presents a general strategy for AD filtering of MR images using an automatic parameter selection method. The basic idea is to estimate the parameters through an optimization step on a synthetic image model, which is different from traditional analytical methods. This approach can be easily applied to more sophisticated diffusion models for better denoising results. We conducted a systematic study of parameter selection for the AD filter, including the dynamic parameter decreasing rate, the parameter selection range for different noise levels and the influence of the image contrast on parameter selection. The proposed approach was validated using both simulated and real MR images. The model image generated using our approach was shown to be highly suitable for the purpose of parameter optimization. The results confirm that our method outperforms most state-of-the-art methods in both quantitative measurement and visual evaluation. By testing on real images with different noise levels, we demonstrated that our method is sufficiently general to be applied to a variety of MR images.     

Prediction of epidemics dynamics on networks with partial differential equations: A case study for COVID-19 in China

Since December 2019, the COVID-19 epidemic has repeatedly hit countries around the world due to various factors such as trade, national policies and the natural environment. To closely monitor the emergence of new COVID-19 clusters and ensure high prediction accuracy, we develop a new prediction framework for studying the spread of epidemic on networks based on partial differential equations (PDEs), which captures epidemic diffusion along the edges of a network driven by population flow data. In this paper, we focus on the effect of the population movement on the spread of COVID-19 in several cities from different geographic regions in China for describing the transmission characteristics of COVID-19. Experiment results show that the PDE model obtains relatively good prediction results compared with several typical mathematical models. Furthermore, we study the effectiveness of intervention measures, such as traffic lockdowns and social distancing, which provides a new approach for quantifying the effectiveness of the government policies toward controlling COVID-19 via the adaptive parameters of the model. To our knowledge, this work is the first attempt to apply the PDE model on networks with Baidu Migration Data for COVID-19 prediction.     

用于数字条纹轮廓术的一种基于广义分析模型的后滤波方法

由于数字投影和采集系统的非线性失真,传统的方法通常需对采集到的条纹进行低通或带通滤波从而抑制高次谐波并获取基频分量。基于广义分析模型针对数字条纹轮廓术提出一种对测量后的物体形貌进行后滤波的算法,消除了非线性失真对测量结果所造成的影响并提高了数字条纹轮廓术的测量精度。论述了条纹轮廓术的原理和广义分析模型,分析推导出后滤波算法。仿真和实验结果表明,后滤波方法能够快速准确地实现基于数字投影的三维形貌重建。     

Simultaneous measurement of rotational and translational diffusion of anisotropic colloids with a new integrated setup for fluorescence recovery after photobleaching

This paper describes an integrated setup for fluorescence recovery after photobleaching (FRAP) for determining translational and rotational Brownian diffusion simultaneously, ensuring that these two quantities are measured under exactly the same conditions and at the same time in dynamic experiments. The setup is based on translational-FRAP with a fringe pattern of light for both the bleaching and monitoring of fluorescently labeled particles, and rotational-FRAP, which uses the polarization of a short bleach light pulse to create a polarization anisotropy. The fringe pattern of the probe beam is modulated in conjunction with a synchronized lock-in amplifier giving a fast, sensitive, ensemble-averaged measurement compared to microscope-image based techniques. The experimental polarization geometry we used ensures that the fluorescence emission is collected without polarization bias. Therefore, only the orientation of the absorption dipole moment of the fixed dye in the particles is measured, which simplifies interpretation of the data. The polarization is modulated rapidly between two orthogonal polarization states, giving the polarization anisotropy in one, single measurement. The rotational and translational Brownian diffusion of anisotropic colloids is measured for ellipsoids of revolution. This experiment shows that in this case the rotational correlation function matches a three-exponential decay in accordance with theoretical predictions.     

A Maximum Entropy Method for Particle Filtering

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.