基于压缩感知和快速波叠加谱方法的近场声全息

在等效源法近场声全息理论的基础上,将等效源强和积分核函数在轴对称虚拟面上进行双向傅里叶级数展开,使待求的源强向量转化为稀疏的傅里叶展开系数向量,并结合压缩感知重构算法中的基追踪降噪算法建立了一种基于压缩感知和快速波叠加谱的半解析、半数值等效源近场声全息方法。利用脉动球源与长条形声源对比了所提方法与传统压缩等效源法的声场重建效果。计算结果表明：当频率较低时,所提方法与传统方法的重建精度相当;但随着频率升高,所提方法的重建精度与抗噪性能均优于传统方法。     

基于算术傅里叶变换的滤波反投影算法的滤波过程的加速

滤波反投影算法是解析法图像重建的经典算法,其加速方法的研究是目前研究的热点之一. 利用算术傅里叶变换和分段卷积的组合可实现滤波加速的方法:首先将斜变滤波器的单位冲激响应分为两段,然后每一段与投影信号采用算术傅里叶变换的方法间接实现线性卷积,最后利用重叠相加法求得滤波投影.实验表明,此方法可以有效地提高滤波反投影算法的运算速度,可比直接卷积的运算速度快390倍,比采用快速傅里叶变换方法的速度快约30%,是一种有效的加速方法.     

适合于两个正交方向的光学层析重建算法

针对常见光学层析重建算法在少投影情况下重建多峰非对称待测场效果差的缺点,本文根据最大熵原理提出了一种适合于两个正交方向的光学层析重建算法.该算法只需要两个正交方向的投影数据就能够获得较好的重建效果.与此同时,由于该算法只需要两个正交方向的投影数据就可较好地完成重建,可使实验系统得到简化,故在重建多峰非对称待测场时表现出了相当的优越性.分别将单峰随机余弦函数、双峰随机余弦函数及三峰随机余弦函数作为待测场进行了计算机数值模拟,并考虑了该算法对噪声的抑制能力.实验结果表明:在施加高斯噪声的情况下,单峰随机余弦待测场的均方根误差降低了62.8%,双峰随机余弦待测场的均方根误差降低了63.3%,三峰随机余弦待测场的均方根误差降低了58.6%.     

二维 Volterra-Fredholm 积分方程数值算法研究及收敛性分析

针对一类二维非线性Volterra-Fredholm积分方程,提出利用二维Block-Pulse函数为基函数进行数值求解。首先,引入Block-Pulse函数的定义及基函数的向量表示形式;其次,根据二维Block-Pulse函数的不相交性和正交性推导了基向量的积分算子矩阵和乘积算子矩阵;然后,基于该算子矩阵将待求问题转化为一系列向量的乘积形式,利用配点法离散未知变量获得原问题的数值解;最后,通过两个具体的数值算例对所提算法的可行性和收敛性进行了验证。     

探测器和投影数目对 CT 重建精度的影响

利用迭代算法从不完全的投影数据中重建图像，得出探测器和投影的数目与图像精度的关系。用琐的探测器数目和旋转角度个数分别进行了图像的重建。在投影数据不完全的条件下，迭代法可以得到较好的重建效果，对于迭代算法，在相同的重建时间内，探测器的数目对图像精度的影响比旋转角度个数的影响要大。     

利用字典学习方法的声速剖面反演研究

针对经验正交函数（Empirical Orthogonal Function,EOF）建模反演得到的声速剖面（Sound Speed Profile,SSP）估计值分辨率比较低的问题,文章采用字典学习方法中的K-奇异值分解（K-Singular Value Decomposition,K-SVD）算法生成声速剖面的非正交原子,研究了该方法生成的学习字典（Learning Dictionary,LD）对声速剖面的重建性能。首先,采用K-SVD算法从获得的数据中训练SSP字典,然后利用正交匹配追踪（Orthogonal Matching Pursuit,OMP）的稀疏方法给出训练信号的稀疏向量,最后通过得到的最优学习字典和稀疏向量反演得到SSP的估计值。结果表明,K-SVD算法比EOF算法使用更少的基函数即可很好地描述SSP的变化,获得更高的反演精度。     

精确型傅里叶高度函数描述子的服装款式识别方法

针对服装款式自动识别时存在提取特征困难、识别率低和分类效率低等问题,该文在精确型傅里叶高度函数(accurate Fourier height functions 2, AFHF2)与线性核函数支持向量机(support vector machine, SVM)基础上提出一种新的服装款式识别方法。首先,利用AHFH2描述子对衣服轮廓进行特征提取,对服装轮廓全局信息和局部信息进行充分表征;然后,在不需要调整参数的情况下使用线性核函数SVM对AFHF2描述子特征进行快速训练与测试。通过自建的服装图形库验证该方法的有效性,实验结果表明该算法优于现有的算法,其中AFHF2描述子优于傅里叶描述子、高度函数(HF)和TCDs等算法,线性核函数SVM算法优于径向基函数SVM算法、K-近邻算法、概率神经网络以及反向传播神经网络算法,其平均识别率能达到97.91%。     

单位冲激抽样序列频谱与傅里叶级数收敛性分析

由傅里叶变换的时移和频移特性,单位冲激抽样序列有两种频谱函数:周期型频谱和级数型频谱,其中周期型频谱函数的推导并不严谨,缺少傅里叶级数收敛性分析。对此提出通过证明两频谱函数等价来验证周期冲激信号傅里叶级数的收敛性。根据脉冲函数定义,运用极限和积分思想,利用抽样函数性质,证明了级数型频谱函数本质是强度和周期均为圆频率的频域冲激序列,验证了冲激抽样序列傅里叶级数的收敛性,周期型频谱函数的傅里叶级数与级数型频谱函数的分析也再次验证了级数的收敛性,但不能验证冲激点不存在吉布斯现象的观点。     

基于固定正交基频谱分析的三维网格模型盲水印算法

为解决基于频率域的三维网格模型数字水印算法中存在的正交基函数不确定性问题,所提算法按网格对偶图构造出固定化的频谱正交基函数,选择一组相似变换不变量作为水印的实际载体,将其投影到固定正交基中实现频谱分解,水印信号隐藏在几个低频系数的线性关系中,提取水印时无需原始网格数据的参与,实验结果表明算法可抵抗平移、旋转、各向一致缩放处理,对低强度的网格几何数据压缩处理和噪声攻击亦具有一定的鲁棒性.     

基于自适应投影增强的压缩感知CT图像重建

针对投影数据受噪声影响严重、被检测工件体积大获取投影数据不完全等导致重建质量差的问题,提出一种自适应反锐化掩模算法对某发动机模拟件投影数据均匀抽取60个角度投影进行预处理,根据其边缘信息设定阈值进行自适应去噪并对高频信息乘以自适应增益增强,采用TV最小化约束的代数重建(ART)算法重建.将改进算法与经典ART、经典反锐化掩模技术处理投影以及投影未处理的POCS-TVM算法进行对比分析,实验结果表明,该方法能够平滑噪声,提高对比度,进而提升不完全投影重建图像质量.重建同样大小的图像,相对于全角度投影迭代一次时间100 s, 60个角度投影迭代一次18.7 s,时间缩短近6倍,大量节省重建时间.     

Accurate image reconstruction from few-view and limited-angle data in diffraction tomography

We present a method for obtaining accurate image reconstruction from highly sparse data in diffraction tomography (DT). A practical need exists for reconstruction from few-view and limited-angle data, as this can greatly reduce required scan times in DT. Our method does this by minimizing the total variation (TV) of the estimated image, subject to the constraint that the Fourier transform of the estimated image matches the measured Fourier data samples. Using simulation studies, we show that the TV-minimization algorithm allows accurate reconstruction in a variety of few-view and limited-angle situations in DT. Accurate image reconstruction is obtained from far fewer data samples than are required by common algorithms such as the filtered-backpropagation algorithm. Overall our results indicate that the TV-minimization algorithm can be successfully applied to DT image reconstruction under a variety of scan configurations and data conditions of practical significance.     

气体浓度层析成像重建算法性能比较与研究

针对少射线成像算法在研究气体浓度层析成像中的重要作用,对常用的几种少射线成像算法的性能进行了详细分析和比较,同时构造了一个多目标函数用于气体浓度优化重建成像。通过实验与常用的几种算法的重建性能相比,多目标优化重建算法具有良好的鲁棒性和抗噪性。在含5%测量误差的情况下,ART 重建结果与原始浓度分布的欧氏距离达 0.1680,而多目标优化重建算法下的该值仅为 0.0325。     

Reconstruction of compact binary images from limited Fourier amplitude data

The problem of reconstructing a binary image from undersampled Fourier amplitude data is considered. This problem maps to an image reconstruction problem in x-ray crystallography. The binary constraint is sufficient to overcome the undersampling and enforce uniqueness, but is insufficient in the case of the additional loss of data that can occur in practice. An iterative projection algorithm is developed that uses binary, connectivity, and compactness constraints to solve the image reconstruction problem. Simulations show the utility of the reconstruction algorithm.     

基于激光投射成像法的管道内壁障碍物检测

提出一种改进的基于激光投射成像法的管道内壁障碍物检测算法。通过激光特征分析与比较法结合提取激光圆环轨迹,利用Otsu算法滤波,最小二乘法确定圆环参数,最后通过离线计算,在线查表方式获得障碍物高度。算法对管道图像亮度无特殊要求,克服了原系统观察与检测不能实时同步的问题。MATLAB运算结果表明:算法的准确性,实时性和鲁棒性相对原设计有了很大的提升。每帧平均运算时间小于0.5s;计算的障碍物高度误差范围?2mm;算法适用于绝大部分场景的管道图片。     

Error dependence of quantized kinoform reconstruction on the position of the desired image

Two-dimensional Fourier transform kinoforms can be calculated by use of a discrete Fourier transform. It is well known that the off-axis reconstruction has lower reconstruction error than the on-axis one. Here we make what to our knowledge is a new analysis on the effect of phase quantization in the Fourier domain. We find that the kinoform reconstruction error changes periodically according to the position of the desired image when a large dummy area is added. The error dependence of quantized kinoform reconstruction is simulated on the position of the desired image by use of the iterative dummy area method and the iterative interlacing technique.     

Multicriteria maximum likelihood neural network approach to positron emission tomography

The emerging technology of positron emission image reconstruction is introduced in this paper as a multicriteria optimization problem. We show how selected families of objective functions may be used to reconstruct positron emission images. We develop a novel neural network approach to positron emission imaging problems. We also studied the most frequently used image reconstruction methods, namely, maximum likelihood under the framework of single performance criterion optimization. Finally, we introduced some of the results obtained by various reconstruction algorithms using computer‐generated noisy projection data from a chest phantom and real positron emission tomography (PET) scanner data. Comparison of the reconstructed images indicated that the multicriteria optimization method gave the best in error, smoothness (suppression of noise), gray value resolution, and ghost‐free images. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol 11, 361–364, 2000     

Two-dimensional inverse born approximation in ultrasonic flaw characterization

A method is developed to characterize flaws of arbitrary shape by using ultrasound pulse echoes at multiple coplanar incident directions. The three-dimensional image reconstruction problem is reduced to a series of two-dimensional image reconstructions, thereby avoiding the difficulties associated with three-dimensional image reconstructions, such as taking and processing a large amount of data, and the complications associated with three-dimensional image reconstructions, such as three-dimensional interpolation, long computing time, etc. The reconstructed two-dimensional images represent the two-dimensional projections or shadows of the three-dimensional flaw characteristic function. Each projection image is reconstructed independently using well-developed computerized tomography reconstruction techniques. If the shape of the flaw is not too irregular, or if the fine details of the shape are not of interest, only a few of these projection images suffice to characterize the flaw. The magnitude scaling problem and the alignment problem of the echoes at different incident directions can be handled easily in the algorithm. Simulation studies yielded encouraging results.     

A modified POCS‐based reconstruction method for compressively sampled MR imaging

One of the challenging tasks in the application of compressed sensing to magnetic resonance imaging is the reconstruction algorithm that can faithfully recover the MR image from randomly undersampled k‐space data. The nonlinear recovery algorithms based on iterative shrinkage start with a single initial guess and use soft‐thresholding to recover the original MR image from the partial Fourier data. This article presents a novel method based on projection onto convex set (POCS) algorithm but it takes two images and then randomly combines them at each iteration to estimate the original MR image. The performance of the proposed method is validated using the original data taken from the MRI scanner at St. Mary's Hospital, London. The experimental results show that the proposed method can reconstruct the original MR image from variable density undersampling scheme in less number of iterations and exhibits better performance in terms of improved signal‐to‐noise ratio, artifact power, and correlation as compared to the reconstruction through low‐resolution and POCS algorithms. © 2014 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 24, 203–207, 2014     

A general gamma nonlinearity compensation method for structured light measurement with off-the-shelf projector based on unique multi-step phase-shift technology

ABSTRACT

Nonlinearities in the application of fringe projection metrology make it very difficult to acquire perfect 3D data. This paper describes a six-step phase-shifting technique for a structured light measurement system with an off-the-shelf projector. First, the phase error is analysed and a gamma model is established by deriving the relative expression between the wrapped phase and input images. This is then expressed in matrix form to derive a unique solution, which is used for the gamma solver. The complex gamma calibration and projector error compensation can be removed once the gamma value of the off-the-shelf projector has been determined. The ideal model reconstruction results are obtained through simulations and experiments, and the standard deviation of the phase error is found to be only 0.0039 radians. Hence, the proposed method eliminates the nonlinear errors associated with fringe projection technology using existing projectors and improves the overall image reconstruction quality.     

基于啁啾脉冲的反射层析激光雷达成像

反射层析激光雷达成像具有系统简单及对湍流不敏感的优势,但普通脉冲发射信号难以兼顾远距离和高精度探测的要求.基于上述情况,本文提出了一种基于啁啾脉冲信号的反射层析激光雷达成像处理方法.该方法首先对啁啾脉冲回波进行相干压缩处理,通过对处理后信号的包络提取得到目标在各方向的反射层析投影数据,最后利用卷积反投影算法实现高分辨力的图像重构.仿真结果表明,在同一投影角度,利用该方法得到的包络与目标反射率投影相一致;在投影角度范围大于60°时能够得到目标的轮廓信息,角度范围越大,成像越精确.研究结果验证了该方法的有效性.