Simultaneous recovery of an infinite rough surface and the impedance from near-field data

In this paper, we consider an inverse rough surface scattering problem in near-field optical imaging. This problem is actually to reconstruct the scattering surface as well as its impedance coefficient from multifrequency near-field data, and can be reduced into an integral scheme by employing an integral representation. We solve this integral scheme by a non-linear integral equation method, and further develop a fast inversion algorithm for reconstructing both the rough surface and the impedance coefficient. Numerical experiments are presented to illustrate the effectiveness of the algorithm.     

The diagonalized contrast source inversion approach for elastic wave inversion

This study focuses on the inverse scattering of objects embedded in a homogeneous elastic background. The medium is probed by ultrasonic sources, and the scattered fields are observed along a receiver array. The goal is to retrieve the shape, location, and constitutive parameters of the objects through an inversion procedure. The problem is formulated using a vector integral equation. As is well-known, this inverse scattering problem is nonlinear and ill-posed. In a realistic configuration, this nonlinear inverse scattering problem involves a large number of unknowns, hence the application of full nonlinear inversion approaches such as Gauss-Newton or nonlinear gradient methods might not be feasible, even with present-day computer power. Hence, in this study we use the so-called diagonalized contrast source inversion (DCSI) method in which the nonlinear problem is approximately transformed into a number of linear problems. We will show that, by using a three-step procedure, the nonlinear inverse problem can be handled at the cost of solving three constrained linear inverse problems. The robustness and efficiency of this approach is illustrated using a number of synthetic examples.     

Development of the methods of analytic regularization in the theory of diffraction

We present a survey of works devoted to the development of the methods of analytic regularization for the solutions of mixed boundary-value problems of the diffraction theory. We consider the problems of diffraction of electromagnetic and acoustic waves on the fragments of conic, wedgelike, and cylindrical perfect surfaces and the problem of diffraction of elastic waves on interface cracks. For the solution of these problems, we develop a method of partial inversion of the operator and apply the Wiener–Hopf technique.     

High-Resolution Digital Integral Photography by use of a Scanning Microlens Array

We suggest what we believe is a new three-dimensional (3-D) camera system for integral photography. Our method enables high-resolution 3-D imaging. In contrast to conventional integral photography, a moving microlens array (MLA) and a low-resolution camera are used. The intensity distribution in the MLA image plane is sampled sequentially by use of a pinhole array. The inversion problem from pseudoscopic to orthoscopic images is dealt with by electronic means. The new method is suitable for real-time 3-D imaging. We verified the new method experimentally. Integral photographs with a resolution of 3760 pixels x 2560 pixels (188 x 128 element images) are presented.     

双相介质二参数反演的同伦方法

研究了同伦方法在双相介质参数反演中的应用。从材料响应的理论合成应与实际测量数据相拟合这一出发点,将参数反演问题转化为非线性算子方程的零点求解问题,然后应用一种大范围收敛的同伦方法求出非线性算子等于零的根作为反问题的解。把这种方法用于Paul(1976)给出的具有解析解的二维双相介质模型的数值模拟,模拟结果表明了同伦反演方法的可行性和稳健性。     

Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color

We present a method to quantify the uncertainties in the in-water constituent absorption and backscattering coefficients obtained from an inversion of remotely sensed reflectance (rrs). We first find a set of positive inversion solutions within a given uncertainty range around the values of the inverted rrs. The uncertainties of the solutions are then computed based on the statistics of these solutions. We demonstrate the uncertainty calculation algorithm using a specific semianalytic inversion model applied to both a field and a simulated data set. When the associated uncertainties are taken into account, the inverted parameters are generally within the uncertainties of the measured (or simulated) parameters, highlighting the success of the inversion and the method to obtain uncertainties. The specific inversion we use, however, fails to retrieve two spectral parameters within a usable range. The method presented is general and can be applied to all existing semianalytical inversion algorithms.     

Determination of particle size distribution by light extinction method using improved pattern search algorithm with Tikhonov smoothing functional

An inversion technique which combines the pattern search algorithm with the Tikhonov smoothing functional for retrieval of particle size distribution (PSD) by light extinction method is proposed. In the unparameterized shape-independent model, we first transform the PSD inversion problem into an optimization problem, with the Tikhonov smoothing functional employed to model the objective function. The optimization problem is then solved by the pattern search algorithm. To ensure good convergence rate and accuracy of the whole retrieval, a competitive strategy for determining the initial point of the pattern search algorithm is also designed. The accuracy and limitations of the proposed technique are tested by the inversion results of synthetic and real standard polystyrene particles immersed in water. In addition, the issues about the objective function and computation time are further discussed. Both simulation and experimental results show that the technique can be successfully applied to retrieve the PSD with high reliability and stability in the presence of random noise. Compared with the Phillips–Twomey method and genetic algorithm, the proposed technique has certain advantages in terms of reaching a more accurate and steady optimal solution with less computational effort, thus making this technique more suitable for quick and accurate measurement of PSD.     

基于波恩近似的二维浅海声层析

目前的海洋声层析方法主要针对深海环境或水平不变浅海环境,对于水平剧变的二维浅海声层析问题仍未提出实用有效的方法。提出一种二维浅海声层析方法并讨论其理论可行性。其主要的思路是将一个水平变化的浅海环境等效为一个水平不变的背景环境叠加微弱的扰动,由波动方程推导出声速扰动与格林函数扰动之间的关系式,引用波恩近似解决两者之间的非线性问题,将反演过程简化为线性方程组的求解过程;后期针对该方法的局限性做进一步改进,包括引入迭代思路及使用一定的先验知识并提取经验正交函数(Empirical Orthogonal Function,EOF)。数值仿真实验说明该方法对局部的小幅度扰动甚至是孤立子内波的反演结果都具有较高的分辨率,初步验证了该方法的理论可行性。     

On the parallelization of unsteady BEM problems with variable mesh size

This paper presents code acceleration strategies for a boundary element method (BEM) simulation of an unsteady free-surface problem with a variable mesh size. The evolution of the film and droplet field emanating from a classical swirl injector/nozzle is used as a test case for the methodology. The unsteady free-surface problem (dynamic grid problem) presents challenges for load balancing the inversion of a matrix that is changing size with time. Since inversion of the matrix of linear equation coefficients represents the dominant computational cost for large problems, the parallelization of the second-order BEM code is implemented using a portable computation library, ScaLAPACK. A different processor grid topology using ScaLAPACK has been implemented and compared to the recommendation of ScaLAPACK guide. Implementation of ScaLAPACK in the solver routine of BEM has been successful and a significant simulation time reduction is demonstrated on an Opteron Dual Processor high-performance computing cluster employing two processors per node.     

基于多模态展开的黏弹性材料复纵波波速反演方法

黏弹性材料广泛应用于水下航行器的降噪、减振或消声,精确获取其动力学参数的需求随着数值仿真技术发展而迅速提升.针对参数获取的声管测量方式,提出了一种使用复反射系数对黏弹性材料复纵波波速快速反演的方法.通过引入多模态展开方法,将复纵波波数超越方程的复平面搜根问题转化为展开系数系统矩阵特征值分解问题,推导出了三种典型背衬情况...     

Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas

We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized forward-scattering operator and leads to the linear inversion formulas that we have reported previously. The higher-order terms represent nonlinear corrections to this result. We illustrate our results with computer simulations in model systems.     

Ultrasonic inverse scattering of multidimensional objects buried in multilayered elastic background structures

The authors focus on the multidimensional inverse scattering of objects buried in an inhomogeneous elastic background structure. The medium is probed by an ultrasonic force and the scattered field is observed along a receiver array. The goal is to retrieve both the geometry (imaging problem) and the constitutive parameters (inverse problem) of the object through an appropriate multiparameter direct linear inversion. The problem is cast in terms of a vector integral equation elastic scattering framework. The multidimensional inverse scattering problem, being nonlinear and ill-posed, is linearized within the Born approximation for inhomogeneous background, and a minimum-norm least-square solution to the discretized version of the vector integral formulation is sought. The solution is based on a singular value decomposition of the forward operator matrix. The method is illustrated on a 2-D problem where constrained least-square inversion of the object is performed from synthetic data. A Tikhonov regularization scheme is examined and compared to the minimum-norm least-square estimate.     

Determination of the optimal regularization parameters in hyperspectral tomography

In a previous paper, we described a novel technique to exploit hyperspectral absorption spectroscopy to retrieve tomographic imaging of temperature and species concentration simultaneously. This technique casts the tomographic inversion into a nonlinear minimization problem with regularizations. Here a simple and effective method is developed to determine the optimal regularization parameters in the nonlinear optimization problem. This method, combined with the minimization method described previously, provides a robust algorithm for hyperspectral tomography. This method takes advantage of an inherent feature of absorption and is therefore expected to be useful for other sensing techniques based on absorption spectroscopy.     

Quasistationary temperature stresses in multiply connected plates in the process of heating

We present an algorithm for the evaluation of quasistationary temperature stresses in multiply connected plates with heat transfer heated by heat sources. For the solution of the problem, we use the Laplace transformation, improved formulas of its numerical inversion, and the method of integral equations. We present several examples of the numerical evaluation of nonstationary temperatures and temperature-induced stresses in plates of various shapes. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 6, pp. 27–33, November–December, 2006.     

An iterative boundary element method for Cauchy inverse problems

 We are interested in this paper in recovering an harmonic function from the knowledge of Cauchy data on some part of the boundary. A new inversion method is introduced. It reduces the Cauchy problem resolution to the determination of the resolution of a sequence of well-posed problems. The sequence of these solutions is proved to converge to the Cauchy problem solution. The algorithm is implemented in the framework of boundary elements. Displayed numerical results highlight its accuracy, as well as its robustness to noisy data. Received 6 November 2000     

Inverse scattering with diffusing waves.

We consider the problem of imaging the optical properties of a highly scattering medium probed by diffuse light. An analytic solution to this problem is derived from the singular value decomposition of the forward-scattering operator, which leads to explicit inversion formulas for the inverse scattering problem with diffusing waves. Computer simulations are used to illustrate these results in model systems.     

Optimal eigenanalysis for the treatment of aerosols in the retrieval of atmospheric composition from transmission measurements

The separation of the individual contributions of aerosol and gases to the total attenuation of radiation through the atmosphere has been the subject of much scientific investigation since remote sensing experiments first began. We describe a new scheme to account for the spectral variation of the aerosol extinction in the inversion of transmission data from occultation measurements. Because the spectral variation of the aerosol extinction is generally unknown,the inversion problem is underdetermined and cannot be solved without a reduction in the number of unknowns in the set of equations used to describe the attenuation at each wavelength. This reduction can be accomplished by a variety of methods, including use of a priori information, the parameterization of the aerosol spectral attenuation, and the specification of the form of the aerosol size distribution. We have developed and implemented a parameterization scheme based on existing empirical and modeled information about the microphysical properties of aerosols. This scheme employs the eigenvectors from an extensive set of simulations to parameterize the aerosol extinction coefficient for incorporation into the inversion algorithm. We examine the accuracy of our method using data sets containing over 24,000 extinction spectra and compare it with that of another scheme that is currently implemented in the Polar Ozone and Aerosol Measurement (POAM) satellite experiment. In simulations using 80 wavelengths in the UV-visible-near-IR spectral range of the Stratospheric Aerosol and Gas Experiment III (SAGE) instrument, we show that, for our optimal parameterization, errors below 1% are observed in 80% of cases, whereas only approximately 20% of all cases are as accurate as this in a quadratic parameterization employing the logarithm of the wavelength.