Deconvolution of complex echo signals by the maximum entropy method in ultrasonic nondestructive inspection

The problem of inversion of convolution with the echo signal point source function is considered with the use of the regularization and maximum entropy method and further reconstruction of two-dimensional images by the method of projection in the spectral domain. The inverse convolution problem is solved for the complex-valued signal that is obtained from the real valued signal through the Hilbert transform. Numerical and experimental simulation is performed. A possibility of enhancing the echo signal along the ray’s resolution and of lowering the spectrum’s noise level with the use of complex signals (pseudo-random sequences) is demonstrated. The results are compared with those obtained using the autoregression method and the reference hologram method.     

On the possibility of using the maximum entropy method in ultrasonic nondestructive testing for scatterer visualization from a set of echo signals

We have studied the possibility of solving the inverse scattering problem in the Born approximation, i.e., the reconstruction of scatterer images from the measured set of echo signals. We have considered generalization of the classical combined SAFT (C-SAFT) algorithm to the case of multiple reflections from uneven boundaries of the tested object taking into account the transformation of the wave type for several positions of the antenna grid, which makes it possible to obtain high-quality scatterer images. Representation of the direct problem in matrix form makes it possible to switch to solving the inverse problem, which can be solved using the Tikhonov regularization procedure, because it is an ill-posed. We have considered the possibility of using the entropy of the image estimate as the stabilizing functional that forms the essence of the maximum entropy method (MEM). The advantage of the MEM over the conventionally used linear C-SAFT method has been shown. The ray model taking into account reflections of rays from the boundaries of the tested object with uneven boundaries has been used for constructing the function estimate. We have demonstrated the ability of the MEM to obtain the scatterer images with superresolution and to suppress the “side lobes” of the function of the point scattering on the collapsed set of echo signals. The use of echo signals reflected from the boundaries of the tested object makes it possible to reconstruct the scatterer shape more exactly. Examples of images reconstructed by the MEM on echo signals obtained in the numerical and model experiments have been presented.     

Application of the maximum entropy method in ultrasound nondestructive testing for scatterer imaging with allowance for multiple scattering

The possibility of solving the inverse scattering problem with allowance for the effect of multiple scattering between the scatterers by the least-squares method that minimizes the solution’s residual is considered. Since the problem is ill-posed, Tikhonov’s regularization is efficient with the entropy of the estimate of the measured field taken as the stabilizing functional, which is the essence of the maximum entropy method. The method is implemented in its multifrequency version. Results of the application of the maximum entropy method in numerical experiments are provided with images reconstructed in different frequency ranges in the presence of white noise.     

二维信号分析法在超声无损检测中的应用

本文综述了近年来二维信号分析法在超声无检测（NDT）中的应用,其中包括二维快速Fourier交换（FFT）、Wigner-Ville分布（WWD）、Gabor变换（GT）和小波变换（WT）等,对它们自在NDT应用中的优缺点进行了分析比较和讨论。     

Characterization of the charge ordering state by maximum entropy method

In this work we introduce the use of a combined Rietveld refinement and Maximum Entropy Method (MEM), as a helpful new tool to gain insight into the charge ordering pattern present in CO-transition metal compounds. In particular we show the study made on two CO oxyborates A₂OBO₃ (A = Mn and Fe): (a) the Mn-oxyborate, that exhibits a strong charge lattice coupling, and whose charge ordering pattern had been previously satisfactory established from BVS analysis of single crystal X-ray diffraction data and that we have used as a test to confirm the validity of the new method; (b) the weakly charge-lattice coupled Fe-oxyborate, a compound not suitable for the BVS approach and for which nevertheless this method gives evidence for a new charge ordering pattern.     

The principle of the maximum entropy method

Abstract

The theoretical background of the maximum entropy method (MEM) when it is applied to restore the electron or nuclear densities from diffraction data is described. In MEM, the concept of “entropy” is introduced to deal with any incompleteness in an observation in a proper way. An incompleteness causes some ambiguities in the results to some extent. The essence of the method is to find a solution which necessarily agrees with the observation, leaving the measure of ambiguities (entropy) maximum. A few results for simple structures with typical types of chemical bonding are also presented.     

A maximum entropy method in spectral estimation

An algorithm is suggested for obtaining estimates of the spectral power density (SPD) of stationary processes, using the Boltzmann definition of entropy. The entropy expression following from this definition differs in the general case from the corresponding expression suggested by Shannon. The reasons for the deviations are revealed.Siberian Physicotechnical Institute, Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 2, pp. 157–162, February, 1991.     

A differential method of maximum entropy

We consider a differential method of maximum entropy that is based on the linearity of Fourier transform and involves reconstruction of images from the differences of the visibility function. The efficiency of the method is demonstrated with respect to the recovery of source images with bright components against the background of a sufficiently weak extended base. The simulation results are given along with the maps of an extragalactic radio source 0059+581, which were obtained using the standard and differential methods of maximum entropy for three observation dates and show that the principle of differential mapping allows us to increase considerably the dynamic interval of images. Institute of Applied Astronomy, Russian Academy of Sciences, St. Petersburg, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 8, pp. 991–998, August, 1998.     

Solution of phase retrieval problem by a maximum entropy method

The phase retrieval problem in image restoration of a spatially bounded source by only the amplitude of its Fourier spectrum is considered. A new algorithm, which is based on the optimization of nonlinear information functionals, and a Shannon entropy functional in particular, is proposed. An idea of combining new algorithms with Fienup iterations is put forward to increase convergence speed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 4, pp. 472–482, April, 1996.     

Analytical methods for modeling of ultrasonic nondestructive testing of anisotropic media

Many modern structural materials exhibit anisotropic elastic behavior leading to complicated wave propagation phenomena. To ensure the reliability of ultrasonic nondestructive testing techniques, these material properties as well as the influence of microstructural inhomogeneities and the effects of interfaces on ultrasonic wave propagation have to be taken into account. In this respect, mathematical modeling provides an efficient method of assisting analysis. Two computationally efficient analytical approaches--a Gaussian beam and a point source superposition technique--are presented, which are well-suited for performing ultrasonic wave propagation and scattering simulations for anisotropic media. Results for homogeneous as well as inhomogeneous anisotropic media like composites and weld material are presented.     

Neutron powder diffraction study of methane deuterohydrate by the maximum entropy method

To examine the nature of thermal motions of the CH₄ molecules in the methane deuterohydrate (8CH₄·46D₂O), the scattering length density distribution was observed by the maximum entropy method (MEM) using neutron powder diffraction data measured in the temperature range of 7-185 K. We drew the scattering-length density distribution as three dimensional graphic images and used the same isosurface level for all temperatures. The negative scattering length density, corresponding to the H atoms of CH₄, was observed only in the large cage. The positive scattering length density attributed to the C atom of CH₄ was observed at the center of each cage. With an increase in temperature, the negative and positive scattering length densities in the large cage disappear. The positive scattering length density remains at the center of the small cage regardless of temperature. These results strongly indicate that the motions of CH₄ depend on the cage size and geometry.     

Semiconductor nondestructive testing by helicon waves

It is shown that the locally excited helicon waves propagate in a semiconductor in terms of a narrow beam. This helicon peculiarity is proposed to be used for the local and contactless measurement of the free charge carrier concentration and mobility as well as the inhomogeneity of their distribution in the material volume. The operating principle of the first helicon tester of the semiconductor electrical homogeneity is presented.     

Spatially resolved ultrasonic attenuation in resistance spot welds: implications for nondestructive testing

Spatial variation of ultrasonic attenuation and velocity has been measured in plane parallel specimens extracted from resistance spot welds. In a strong weld, attenuation is larger in the nugget than in the parent material, and the region of increased attenuation is surrounded by a ring of decreased attenuation. In the center of a stick weld, attenuation is even larger than in a strong weld, and the low-attenuation ring is absent. These spatial variations are interpreted in terms of differences in grain size and martensite formation. Measured frequency dependences indicate the presence of an additional attenuation mechanism besides grain scattering. The observed attenuations do not vary as commonly presumed with weld quality, suggesting that the common practice of using ultrasonic attenuation to indicate weld quality is not a reliable methodology.     

金属增材制件的超声无损检测与评价研究进展

金属增材制件在航空航天、核电等高端领域应用日益广泛,及时获取缺陷和微观组织结构信息,对改进制造过程、保证产品质量和相关设备的安全稳定运行具有重要意义。然而,特殊的制造工艺导致金属增材制件内部晶粒粗大,组织各向异性复杂,声波衰减严重,给超声检测带来了很大挑战。该文简要梳理了金属增材制造过程中常见的缺陷类型和成型件微观组织结构特征;从传统水浸式超声检测、相控阵超声检测和激光超声检测3个方面,重点论述了超声检测技术在金属增材制件缺陷检测领域的应用现状;提出基于超声检测技术无损评价金属增材制件微观组织结构和力学性能的原理以及评价模型建立方法,并对相关重难点做了阐述;最后总结了超声无损检测技术在金属增材制件质量评价领域应用中面临的挑战和发展趋势,并对未来应重点关注的研究方向给出建议。     

Time-dependent radiative transfer using Chapman-Enskog maximum entropy method

The time-dependent problems of radiative transfer involve a coupling between radiation and material energy fields and are nonlinear because of proposed temperature dependence of the medium characteristics in semi-infinite medium with Rayleigh anisotropic scattering. By means of the limited flux, Chapman-Enskog and maximum entropy technique the time-dependent radiative transfer equation has been solved explicitly. The maximum entropy method is used to solve the resulting differential equation for radiative energy density. The calculations are carried out for temperature (normalized dimensionless) Θ(x,τ), radiative energy density and net flux with Rayleigh and anisotropic scattering for different space at different times.     

基于最大模糊熵和遗传算法的图像分割

为了分割照度不均匀的网格图像,提出了一种基于最大模糊熵和遗传算法的阈值分割方法。基于模糊集合理论,根据像素灰度值把原始图像中的像素分为黑和亮两个模糊集,利用最大模糊熵准则确定模糊区间的范围,寻找模糊参数的最优组合,实现图像分割。由于穷举法搜索模糊参数的最优组合存在计算复杂度高、占用存储空间大等缺点,因此采用了遗传算法确定最优阈值。为了验证该方法的有效性,对其进行了图像分割实验,并与最大类间方差法、迭代法和一维最大熵法进行了比较。实验结果表明,该方法能够自动、有效地选取阈值,分割效果优于其它三种算法,并能保留原始图像的主要特征。     

最大熵法在风廓线雷达谱分析中的应用研究

为了解现代谱分析技术在风廓线雷达中应用的可行性,通过采用实测的和模拟的风廓线雷达回波信号,对比研究了FFT法与最大熵法的谱分析效果。结果表明:(1)当回波信号比较强时,两者都可以得到较好的谱分析效果;但是当回波信号较弱时,最大熵法分析效果优于FFT法,最大熵法对地杂波具有较好的抑制能力。(2)最大熵谱比较光滑,表明最大熵法对随机白噪声也有一定的抑制作用。(3)最大熵法的递推阶数对谱分析结果有一定影响,最终预测误差准则确定的递推阶数一般偏小,采用15阶的递推阶数进行最大熵法分析取得了较好结果。由于风廓线雷达回波通常都较弱,因此研究结果可望用于改善信号处理效果。     

管材超声探伤中缺陷模糊模式识别方法研究

本文探讨了对管材缺陷形状进行模糊模式识别的一种方法。提出并研究了管材超声探伤中缺陷模糊模式识别的物理模型,模糊模式的特征参数选择原则和方法,建立了三种缺陷的标准模糊子集,并运用模糊模式识别的数学方法对大量人工缺陷的实验数据进行了数值计算,获得了预想的结果。     

Analysis of fluorescence decay kinetics of thioflavin t by a maximum entropy method

The application of a maximum entropy method (MEM) for analysis of time-resolved fluorescence data is discussed. A developed version of MEM has been tested using simulated kinetic data. Based on computed results, practical criteria have been established to determine whether the lifetime distribution of emitting centers is described by a discrete spectrum (a set of two or three exponentials) or by a continuous one (mono- or bimodal distribution of exponentials). The proposed method has been used to analyze the fluorescence decay kinetics of thioflavin T (ThT) intercalated into amyloid fibrils. The presence of two peaks in the lifetime distribution of emitting centers has been explained by the existence in fibrils of two types of binding centers substantially differing in microenvironment rigidity. This suggestion is supported by the results of fluorescence quenching of intercalated ThT with the quencher KI.