Image quality improvement in ultrasonic nondestructive testing by the maximum entropy method

We consider the possibility of solving the inverse scattering problem in the linear approximation (in the form of a convolution equation) by reducing it to a system of linear algebraic equations and minimizing the residual. Since the problem is an ill-posed one, the Tikhonov regularization proves useful. The possibility of using the entropy of the image estimate as a stabilizing functional is considered, which is the key idea of the maximum entropy method. The single-frequency and multifrequency versions of the method are realized. The advantage of the maximum entropy method over the conventional linear methods of solving the inverse scattering problem is shown. The superresolution and sidelobe suppression abilities of the maximum entropy method are demonstrated. The method is shown to be stable to measurement noise and multiplicative interference in the form of aperture decimation. Examples of the image reconstruction by the maximum entropy method from model and experimental data are presented.     

激光聚变中存在吸收的图像重建

提出了一种处理激光等离子体中含吸收的图像重建方法,且运用最大熵原理推导出适用于含吸收的重建算法,采用不同的图像实例进行模拟计算,结果表明采用吸收校正方法的精度明显高于不考虑吸收校正的精度。     

Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures

The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms provide significant improvements over transform methods in computed tomography. In this paper, we present an extended class of power-divergence measures (PDMs), which includes a large set of distance and relative entropy measures, and propose an iterative reconstruction algorithm based on the extended PDM (EPDM) as an objective function for the optimization strategy. For this purpose, we introduce a system of nonlinear differential equations whose Lyapunov function is equivalent to the EPDM. Then, we derive an iterative formula by multiplicative discretization of the continuous-time system. Since the parameterized EPDM family includes the Kullback–Leibler divergence, the resulting iterative algorithm is a natural extension of the maximum-likelihood expectation-maximization (MLEM) method. We conducted image reconstruction experiments using noisy projection data and found that the proposed algorithm outperformed MLEM and could reconstruct high-quality images that were robust to measured noise by properly selecting parameters.     

Omega-space adaptive acquisition technique for magnetic resonance imaging from projections

An omega-space adaptive acquisition technique for MRI from projections is presented. It is based on the evaluation of the information content of a set composed of four initial projections, measured at angles 0 degrees, 45 degrees, 90 degrees, and 135 degrees, followed by the selection of new angles where the information content is maximum. An entropy function is defined on the power spectrum of the projections that is useful for evaluating the information content of each projection. The method makes it possible to reduce the total acquisition time with little degradation of the reconstructed image and it adapts to the arbitrary shape of the sample. For this reason, it can be particularly useful in those applications where acquisition from projections is strongly recommended to save acquisition time, such as functional MRI, imaging of species having very short T(2), or angiography. The method has been tested both on simulated data and on experimental data collected by a commercial MRI apparatus. The method has also been compared to the regular acquisition method, that is, the standard acquisition method in MRI from projections.     

Progressive EPR imaging with adaptive projection acquisition

Continuous wave electron paramagnetic resonance imaging (EPRI) of living biological systems requires rapid acquisition and visualization of free radical images. In the commonly used multiple-stage back-projection image reconstruction algorithm, the EPR image cannot be reconstructed until a complete set of projections is collected. If the data acquisition is incomplete, the previously acquired incomplete data set is no longer useful. In this work, a 3-dimensional progressive EPRI technique was implemented based on inverse Radon transform in which a 3-dimensional EPR image is acquired and reconstructed gradually from low resolution to high resolution. An adaptive data acquisition strategy is proposed to determine the significance of projections and acquire them in an order from the most significant to the least significant. The image acquisition can be terminated at any time if further collection of projections does not improve the image resolution distinctly, providing flexibility to trade image quality with imaging time. The progressive imaging technique was validated using computer simulations as well as imaging experiments. The adaptive acquisition uses 50-70% less projections as compared to the regular acquisition. In conclusion, adaptive data acquisition with progressive image reconstruction should be very useful for the accelerated acquisition and visualization of free radical distribution.     

Fast Estimation of Scatter Components Using the Ordered Subset Expectation Maximization Algorithm for Scatter Compensation

In this work we propose a method for scatter compensation in single photon emission computed tomography imaging, by which we can estimate the scatter components in projections in high speed with good accuracy. The method is that we first estimate the scatter components in projections based on scatter response kernels by one time of ordered subsets expectation maximization iterative reconstruction, and then subtract the estimated scatter components from the projections and complete reconstruction by filtered back-projection method. The principle is that the image corresponding to the scatter components in projections consists largely of low-frequency components of an activity distribution; these low-frequency components will converge faster than the high ones in iterative reconstruction. Therefore, we can estimate the low-frequency component image before the image converges with the high-frequency ones, and obtain the scatter components by re-projecting the low-frequency component image with scatter response kernels. The effects of the proposed method were compared with the dual- and triple-energy window methods using experimental measurements. The results show that good accuracy in estimated scatter components, good uniformity of scatter compensation at the center and the side of an object, and good noise property can be acquired by this method.     

浓度场测量的差分吸收光谱CT技术

提出了一种新的用于浓度场测量的差分吸收光谱CT技术。利用差分吸收原理进行浓度场多方位积分测量,采用少数投影最大熵重建算法进行层析图像重建。数值模拟结果表明,在0°～180°视场范围内,在4个不同的投影视角方向获取投影数据的条件下,能有效地重建出待测场分布。该技术具有较高的重建精度和良好的抗噪声性能。     

多金属物体CT图像的金属伪影校正

针对多金属伪影的校正问题,本文通过仿真实验分析了多金属伪影的成因,并提出了一种基于投影校正的多金属伪影校正方法.该方法首先直接从投影域分割出金属区域,然后建立对金属区域投影值的校正模型,最后通过调整模型参数达到校正目的.模型以重建图像的灰度熵为目标函数,采用单纯形法迭代求解使熵最小时的校正参数.仿真和实际数据的实验结果表明,本文算法对多金属伪影的校正起到了良好的效果,且校正后的图像质量优于插值校正法.     

A modified equally sloped algorithm based on the total variation algorithm in computed tomography for insufficient data

Computed tomography (CT) has become an important technique for analyzing the inner structures of material, biological and energy fields. However, there are often challenges in the practical application of CT due to insufficient data. For example, the maximum rotation angle of the sample stage is limited by sample space or image reconstruction from the limited number of views required to reduce the X‐ray dose delivered to the sample. Therefore, it is difficult to acquire CT images with complete data. In this work, an iterative reconstruction algorithm based on the minimization of the image total variation (TV) has been utilized to develop equally sloped tomography (EST), and the reconstruction was carried out from limited‐angle, few‐view and noisy data. A synchrotron CT experiment on hydroxyapatite was also carried out to demonstrate the ability of the TV‐EST algorithm. The results indicated that the new TV‐EST algorithm was capable of achieving high‐quality reconstructions from projections with insufficient data.     

基于三投影方向的层析重建分析

针对传统的层析方法中,投影方向多、系统复杂等特点,提出了基于三个投影方向的层析重建方法.论文选取适用于少投影方向的代数迭代重建算法,采用参量修正方法,能较好的提高重建准确度和抑制椒盐噪音.同时对影响重建图像质量和速度的迭代次数、不同原图像结构对重建图像质量的影响进行了分析,给出了相应分析模拟结果.结果表明,迭代300次后,重建结果基本稳定.同时对于具有轴对称结构物体,三个方向投影数据能够较好地实现三维层析重建.分析结果为后期开展的基于单幅层析全息图的三维层析重建实验研究提供了理论依据.     

基于稀疏优化的计算机断层成像图像不完全角度重建综述

计算机断层成像(computed tomography,CT)技术在医学和工业无损检测中都具有非常广泛的应用,CT重建算法是其中的核心,而不完全角度重建问题则是实际应用中重建算法研究领域的一个热点和难点问题.近年来,随着稀疏优化理论与算法的飞速发展,基于稀疏优化的重建算法已经在不完全角度重建问题中得到了较广泛的应用,且表现出了良好的精度与速度性能.本文首先对稀疏优化的基本理论结论与常用算法进行了介绍;而后对稀疏优化理论在CT图像不完全角度重建中的应用进行归纳,分类介绍了其主要研究成果及稀疏优化所发挥的作用;最后对基于稀疏优化的不完全角度重建研究进行了展望.     

H2O温度二维分布的滤波反投影重建

利用可调谐半导体吸收光谱技术实现燃烧场温度二维分布重建。设计H2O模型温度分布范围为300~1300 K,高斯型分布,利用Radon变换模拟实验测量结果。采用滤波反投影算法重建了两条吸收谱线强度场,进而得到气体温度二维分布,重建结果与模型符合较好。研究了不同投影数目和随机噪声对重建结果的影响,结果表明：随着投影数目的减少和噪声幅值的增加,重建温度分布均方误差增大,图像重建效果变差。当投影数目减小到4个,重建温度场已不能完全反映原始温度场信息。     

H2O温度二维分布的滤波反投影重建

利用可调谐半导体吸收光谱技术实现燃烧场温度二维分布重建。设计H2O模型温度分布范围为300~1300 K,高斯型分布,利用Radon变换模拟实验测量结果。采用滤波反投影算法重建了两条吸收谱线强度场,进而得到气体温度二维分布,重建结果与模型符合较好。研究了不同投影数目和随机噪声对重建结果的影响,结果表明:随着投影数目的减少和噪声幅值的增加,重建温度分布均方误差增大,图像重建效果变差。当投影数目减小到4个,重建温度场已不能完全反映原始温度场信息。     

An algorithm for computed tomography image reconstruction from limited-view projections

<正>With the development of the compressive sensing theory,the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology.This paper develops an iterative algorithm for image reconstruction,which can fit most cases.This method gives an image reconstruction flow with the difference image vector,which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough.Then the l_2-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles.The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data.Moreover,all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.     

基于联合正则化及压缩传感的MRI图像重构

基于压缩传感的MRI图像重构利用图像稀疏的先验知识能从很少的投影值重构原图像。目前MRI重构算法只利用MRI图像稀疏性表示或只利用基于其局部光滑性的先验知识,重构效果不理想。针对此问题,结合两种先验知识,提出一种基于联合正则化及压缩传感的MRI图像重构方法。利用块坐标下降法将求解联合正则化问题转化为交替求解二次凸优化、稀疏正则化和全变差正则化三个简单的优化问题。并提出分别采用共轭梯度法、二元自适应收缩法以及梯度下降法对以上优化问题求解。实验结果表明,该算法重构效果比现有算法有明显地提高。     

乘代数重建法和最大熵重建法比较研究

本文从最大熵原理引入拉格朗日因子推导出乘代数重建法(MART)和最大熵重建法(MENT),同时他们是等价的,只是迭代方法不同而已。而且用实例进行模拟计算,计算结果也表明这两种方法收敛情况和重建精度完全一致,从而进一步证明MART和MENT的等价性。     

Comparison of maximum entropy and filtered back-projection methods to reconstruct rapid-scan EPR images

Reconstruction of two-dimensional images by filtered back-projection (FBP) and by the maximum entropy method (MEM) was compared for spectral-spatial EPR images with differing signal-to-noise ratios. Experimental projections were recorded using direct-detected rapid scans in the presence of a series of magnetic field gradients. The slow-scan absorption lineshapes were calculated by Fourier deconvolution. A Hamming filter was used in conjunction with FBP, but not for MEM. Imperfections in real experimental data, as well as random noise, contribute to discrepancies between the reconstructed image and experimental projections, which may make it impossible to achieve the customary MEM criterion for convergence. The Cambridge MEM algorithm, with allowance for imperfections in experimental data, produced images with more linear intensity scales and more accurate linewidths for weak signals than was obtained with another MEM method. The more effective elimination of noise in baseline regions by MEM made it possible to detect weak trityl (13)C trityl hyperfine lines that could not be distinguished from noise in images reconstructed by FBP. Another advantage of MEM is that projections do not need to be equally spaced. FBP has the advantages that computational time is less, the amplitude scale is linear, and there is less noise superimposed on peaks in images. It is useful to reconstruct images by both methods and compare results. Our observations indicate that FBP works well when the number of projections is large enough that the star effect is negligible. When there is a smaller number of projections, projections are unequally spaced, and/or signal-to-noise is lower MEM is advantageous.     

Maximum entropy analysis of coded images

Maximum entropy reconstruction of coded images which are very noisy or consist of only a small number of detected quanta is considered. It is shown that for data with a high constant variance noise background, maximum entropy allows useful images to be reconstructed from data that is otherwise too noisy. The maximum entropy principle is also applied to quantum limited data where an approach for finding the optimum smoothing is developed which allows information about the location and outline of the object to be deduced from very sparse data. In the neutron imaging example presented, this was done with only 715 detected quanta.     

一种光学层析图像的多准则重建方法

光学层析成像是一个病态重建问题,为克服重建过程的病态性,提出将多准则优化理论引入到图像重建中。利用了三个用于光学层析图像重建的准则:平方误差函数、图像熵函数和局部平滑函数。采用向量优化方法将多准则优化问题转化为单准则优化问题求解。为了确定各个目标函数间的权重系数,提出一种动态权重系数求解方法。重建过程目标函数关于光学参量的梯度计算是关键,因此提出一种基于梯度树的计算方法。实验过程中对多准则重建结果和基于平方误差函数的单准则重建结果做了比较,证明该方法能够克服传统的偏重单一目标的单准则重建的不足,有效地重建光学层析图像,提高图像重建质量。     

采样间隔和投影数对SR-XFMT重构质量的影响

同步辐射微束X射线荧光CT(SR-XFMT)是一种能无损、高空间分辨和高灵敏地探测样品内部元素含量和分布的新技术. 对SR-XFMT实验进行了计算机模拟, 讨论了采样间隔和投影数对重构质量的影响, 分析发现采样间隔对重构质量的影响比投影数的影响要大.