Application of the nonregularization method to solving the inverse problem of passive acoustic thermotomography on the wavelet basis

A comparative analysis of reconstruction quality is performed for the reconstruction of the temperature distribution under hyperthermia by the regularization and nonregularization methods, which are used for solving the systems of linear equations following from the statement of the ill-posed inverse problem of passive acoustic thermotomography. The basis functions are chosen to be wavelets, which allows a compact representation of the temperature peak under reconstruction. It is shown that, when deep-seated parts of tissue are heated, the nonregularization method gives a much smaller systematic error of temperature reconstruction at the focusing point. At the same time, the random error of reconstruction increases. The nonregularization method of reconstruction can be used in combination with regularization for monitoring hyperthermia procedures in oncology to obtain more detailed information on the in-depth temperature.     

三维复杂温度场高精度声学测量方法

声学温度场检测技术通过多路径声波传播时间数据,反演被测区域的温度分布.提供了一种高精度的三维复杂温度场的声学测量方法.首先从射线声学角度给出了三维非均匀温度场中声波传播路径的数学模型.在此基础上,将三维温度场的重建问题转化为声波传播路径的求解和温度场的反演问题,建立了基于多项式修正径向基函数(RBF-PR)和改进的Ti...     

Standard source method in passive acoustic thermal tomography

Potentialities of passive acoustic thermal tomography in reconstructing the 2D temperature distribution in a human body are studied. Special attention is given to the estimation of the maximal temperature value. A method for its exact reconstruction is proposed. The method uses the assumption that the temperature distribution is formed by a local heat source and is based on the selection of the parameters of such a source by the minimization of the residual of the measured and hypothetical values of the acoustic brightness temperature. The accuracy of the determination of the maximal in-depth temperature by different methods is analyzed by numerical simulation. It is demonstrated that the proposed method provides a higher accuracy than Tikhonov’s methods of global and local regularization, especially with a heat source at great depth. The proposed method is shown to cause no systematic error in the reconstruction of temperature peaks at great depth. The possibility of reconstructing a two-peak temperature distribution by the proposed method is demonstrated.     

二维小波变换及在青藏高原地形重构中的应用

计算和检验了4种不同小波基底和不同阶小波基底对单脉冲和尖峰两个信号的分解及重构的性质,结果表明双正交小波的精度最高,Coifman小波的精度最低.通过设阈值对小波和快速Fourier变换进行截断后再重构,说明小波具有重构精度高、所用非零系数少以及误差被局域化等优点,这就削弱了"Gibbs现象",限制了它的影响范围.在此基础上,用二维快速Fourier和二维离散小波变换对实际青藏高原及其附近地形做了分解、重构及截断后重构等,说明二维小波变换能以较之FFT更少的非零系数和误差局域化等重构大地形,表明了二维小波变换在未来大气环流数值模式中的应用潜力.     

A forward model and conjugate gradient inversion technique for low-frequency ultrasonic imaging

Emerging methods of hyperthermia cancer treatment require noninvasive temperature monitoring, and ultrasonic techniques show promise in this regard. Various tomographic algorithms are available that reconstruct sound speed or contrast profiles, which can be related to temperature distribution. The requirement of a high enough frequency for adequate spatial resolution and a low enough frequency for adequate tissue penetration is a difficult compromise. In this study, the feasibility of using low frequency ultrasound for imaging and temperature monitoring was investigated. The transient probing wave field had a bandwidth spanning the frequency range 2.5-320.5 kHz. The results from a forward model which computed the propagation and scattering of low-frequency acoustic pressure and velocity wave fields were used to compare three imaging methods formulated within the Born approximation, representing two main types of reconstruction. The first uses Fourier techniques to reconstruct sound-speed profiles from projection or Radon data based on optical ray theory, seen as an asymptotical limit for comparison. The second uses backpropagation and conjugate gradient inversion methods based on acoustical wave theory. The results show that the accuracy in localization was 2.5 mm or better when using low frequencies and the conjugate gradient inversion scheme, which could be used for temperature monitoring.     

Absorption and emission of electron cyclotron waves in plasmas with electron momentum anisotropies both along and across the external magnetic field

Summary A simple and compact form is given to dielectric tensor and ?local emission temperature? for electron cyclotron waves in hot magnetoactive plasmas of thermonuclear interest, containing electron populations with a wide range of possible momentum anisotropies. An analytical model is presented for the representation of electron distributions exhibiting flat suprathermal tails along the external magnetic field and applied to the computation of the pertinent absorption and emission coefficients.     

Ultrasonic imaging of an object at the presence of Fourier and non-Fourier transformation in the transmitted through the object acoustic field

A metal object is computer visualized by registration of the amplitudes of the transmitted through the object short acoustic pulses. The pulses are separated by time, because of the presence of holes and internal compact components in the longitudinal section (structure along the propagation direction of acoustic wave). The acoustic field transmitted through the object is composited from a field presenting Fourier transformation of the hole shape and field, transmitted through the metal components in the longitudinal section of the object. A computer Fourier transformation of the digital data of the amplitude fields transmitted through the object components is performed instead of converging lens. The Fourier series of the object obtained as digital data after the transformation is multiplied with a term, describing the angle distribution of the field on spatial frequencies. The reconstruction of the image of the metal components is performed by reverse transformation, i.e. summing up in all spatial frequencies. 3D visualization of the transmitted through the hole acoustic field determines the hole geometry (circular, square, rectangular).It is shown that at the transmission of a short acoustic pulse through the components with different thicknesses and holes, presenting Fourier and non-Fourier transformation can be registered separately in contrast to the optics.     

Tomographic reconstruction of atmospheric turbulence with the use of time-dependent stochastic inversion

Acoustic travel-time tomography allows one to reconstruct temperature and wind velocity fields in the atmosphere. In a recently published paper [S. Vecherin et al., J. Acoust. Soc. Am. 119, 2579 (2006)], a time-dependent stochastic inversion (TDSI) was developed for the reconstruction of these fields from travel times of sound propagation between sources and receivers in a tomography array. TDSI accounts for the correlation of temperature and wind velocity fluctuations both in space and time and therefore yields more accurate reconstruction of these fields in comparison with algebraic techniques and regular stochastic inversion. To use TDSI, one needs to estimate spatial-temporal covariance functions of temperature and wind velocity fluctuations. In this paper, these spatial-temporal covariance functions are derived for locally frozen turbulence which is a more general concept than a widely used hypothesis of frozen turbulence. The developed theory is applied to reconstruction of temperature and wind velocity fields in the acoustic tomography experiment carried out by University of Leipzig, Germany. The reconstructed temperature and velocity fields are presented and errors in reconstruction of these fields are studied.     

Connection between Group Based Quantum Tomography and Wavelet Transform in Banach Spaces

The intimate connection between the Banach space wavelet reconstruction method for each unitary representation of a given group and some of well known quantum tomographies, such as: tomography of rotation group, Spinor tomography and tomography of Unitary group, is established. Also both the atomic decomposition and Banach frame nature of these quantum tomographic examples is revealed in details.     

Acoustothermometric study of the human hand under hyperthrmia and hypothermia

The results of an acoustothermometric study of the human hand under local hyperthermia and hypothermia are presented. Individuals under testing plunged their hands in hot or cold water for several minutes. Thermal acoustic radiation was detected by two sensors placed near the palm and near the backside of the tested hand. The internal temperature profiles of the hand were reconstructed. The indirect estimate of the reconstruction error was 0.6°C, which is acceptable for medical applications. Hyperthermia was achieved by placing the hand in water with a maximal temperature of 44°C for 2 min. In this case, the internal temperature was 35.4 ± 0.6°C. Hypothermia was achieved by placing the hand in water with a temperature of 17.8°C for 15 min. In this case, the internal temperature decreased from 26 to 24°C. The use of a four-sensor planar receiving array allowed dynamic mapping of the acoustic brightness temperature of the hand.     

声学CT复杂温度场重建研究

为提高声学CT复杂温度场重建能力,提出一种利用Markov径向基函数逼近和Tikhonov正则化的温度场重建算法,简称MTR算法。该算法首先用Markov径向基函数的线性组合,逼近介质中的复杂声速场分布,然后利用介质中多路径声波传播时间和Tikhonov正则化法,求解声速场分布,进而利用声速与温度的关系获得温度分布。对单热点、三热点和五热点温度场模型进行了仿真重建,结果表明MTR算法热点定位精度高,重建误差小。开发了声学CT温度场重建实验系统,用电加热器在内装1200 kg大豆的实验粮仓中形成热点,MTR重建结果能正确反映热点位置,热点温度重建误差1.3%。可见,MTR算法复杂温度场重建能力强,可望用于实际储粮温度分布监测。      

Application of acoustic reflection tomography to sonar imaging

Computer-aided tomography is a technique for providing a two-dimensional cross-sectional view of a three-dimensional object through the digital processing of many one-dimensional views (or projections) taken at different look directions. In acoustic reflection tomography, insonifying the object and then recording the backscattered signal provides the projection information for a given look direction (or aspect angle). Processing the projection information for all possible aspect angles enables an image to be reconstructed that represents the two-dimensional spatial distribution of the object's acoustic reflectivity function when projected on the imaging plane. The shape of an idealized object, which is an elliptical cylinder, is reconstructed by applying standard backprojection, Radon transform inversion (using both convolution and filtered backprojections), and direct Fourier inversion to simulated projection data. The relative merits of the various reconstruction algorithms are assessed and the resulting shape estimates compared. For bandpass sonar data, however, the wave number components of the acoustic reflectivity function that are outside the passband are absent. This leads to the consideration of image reconstruction for bandpass data. Tomographic image reconstruction is applied to real data collected with an ultra-wideband sonar transducer to form high-resolution acoustic images of various underwater objects when the sonar and object are widely separated.     

层析成像图像重建算法综述

介绍了层析成像技术的图像重建算法,并从正向问题数学模型的简化和反向问题数学模型的映射结构的角度比较了各种算法的特点和优劣。研究表明:用本质是线性算法的各种变换方法重建图像存在严重失真,而卷积滤波的引入可以使变换方法的重建效果有所改善;基于导数搜索的迭代算法对初始值依赖性强、收敛速度慢并且容易陷入局部最优解;基于Fourier变换的方法具有本质的局限性;小波变换则可以同时刻画图像时域和频域的细节特征;有限元法通过重建对象像素的智能划分可以简化正问题的复杂性;而具有物理背景的蒙特卡罗法、模拟退火法、遗传算法、粒子滤波法及神经网络法更适合于复杂且非线性的图像重建;智能化、仿生化、并行化以及各种算法的融合是层析成像图像重建算法的发展趋势。     

Flame four-dimensional deflection tomography with compressed-sensing-revision reconstruction

Deflection tomography with limited angle projections was investigated to visualize a premixed flame. A projection sampling system for deflection tomography was used to obtain chronological deflectogram arrays at six view angles with only a pair of gratings. A new iterative reconstruction algorithm with deflection angle compressed-sensing revision was developed to improve reconstruction-distribution quality from incomplete projection data. Numerical simulation and error analysis provided a good indication of algorithm precision and convergence. In the experiment, 150 fringes were processed, and temperature distributions in 20 cross-sections were reconstructed from projection data in four instants. Four-dimensional flame structures and temperature distributions in the flame interior were visualized using the visualization toolkit. The experimental reconstruction was then compared with the result obtained from computational fluid dynamic analysis.     

Comparison of results of interferometric phase extraction algorithms for three-dimensional flow-field tomography

A comparison of the results of interferometric phase information retrieval and subsequent tomographic reconstruction from deformed wavefront projections by phase unwrapping is presented. In interferogram processing, conventional fringe tracking and Fourier transform methods have been utilized for comparison. With these methods by injecting carrier fringes, the projection data of any axial cross section can be extracted in all projection directions to implement three-dimensional tomographic reconstruction. The results of experiments of a simulated temperature field prove that the phase extraction based on the Fourier transform method produces tomographic reconstruction much superior to the conventional fringe tracking technique.     

一种考虑声线弯曲的温度场重建算法

声波在非均匀温度场中传播时会由于声波的折射而产生声线弯曲现象。为提高非均匀温度场声学CT (Computer Tomography)重建精度,提出一种考虑声线弯曲的重建算法。首先用最小二乘法获得一个不考虑声线弯曲的重建温度场,然后用打靶-插值法确定本征声线出射角,用三角形前向展开法追踪声线,获得此温度场中声波发射/接收器间的本征声线,建立本征声线上声波传播时间与温度分布间的关系,进而实现考虑声线弯曲的最小二乘法温度场重建。单峰、双峰温度场仿真重建结果表明:所采用的本征声线追踪法计算简单运行速度快;考虑声线弯曲后,可明显提高温度场重建精度。因此所提重建算法能更好地适应实际温度场重建需求。      

A computer simulation study of imaging flexural inhomogeneities using plate-wave diffraction tomography

This paper investigates the feasibility of plate-wave diffraction tomography for the reconstruction of flexural inhomogeneities in plates using the results of computer simulation studies. The numerical implementation of the fundamental reconstruction algorithm, which has recently been developed by Wang and Rose [C.H. Wang, L.R.F. Rose, Plate-wave diffraction tomography for structural health monitoring, Rev. Quant. Nondestr. Eval. 22 (2003) 1615-1622] is investigated addressing the essential effects of applying the discrete form of the Fourier diffraction theorem for solving the inverse problem as discussed by Kak and Slaney [A.C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging, IEEE Press, New York, 1988] for the acoustic case, viz. diffraction limited sensitivity, influence of weak scatterer assumption, damage location and scatter field data processing in time and Fourier space as well as experimental limitations such as finite receiver length and limited views. The feasibility of the imaging technique is investigated for cylindrical inhomogeneities of various severities and relative position within the interrogation space and a normal incident interrogation configuration. The results show that plate-wave diffraction tomography enables the quantitative reconstruction of location, size and severity of plate damage with excellent sensitivity and offers the potential for detecting corrosion thinning, disbonds and delamination damage in structural integrity management applications.     

多光谱辐射层析重建三维火焰温度场

提出一种基于多光谱辐射测温理论及光学层析技术的三维温度场重建方法。建立了基于参考温度的多光谱测温法数学模型，提出了一种基于模拟退火理论的变松弛因子的光学层析技术新算法，通过计算机数值模拟，详细考察了该算法对非对称温度场分布的重建效果并与传统的代数迭代重建算法及滤波反投影算法进行比较。计算结果表明，变弛豫因子重建算法重建精度最高。作为一个应用实例，用多光谱辐射变弛豫因子重建层析方法重建了四峰蜡烛火焰某一截面的温度分布。     

根据稀疏基底选择抽样模型

在压缩传感技术应用中,根据稀疏基底选择抽样模型对重构结果影响很大。在傅里叶空间中,极坐标星形抽样和随机抽样的重构效果差异巨大,应用傅里叶光学理论对傅里叶空间的频谱分布进行分析,从理论上解释了原因,并且据此提出稀疏基底和抽样模型的匹配情况会影响重构效果。在小波空间中,进行了均匀抽样和随机抽样的对比重构实验,发现后者的重构效果更好,并确定了根据稀疏基底选择合适抽样模型的可行性,为实际应用中降低抽样率,提高重构效果提供了方法依据。