基于改进SR3模型算法的ECT图像重建研究

针对电容层析成像技术应用于气固两相流检测时,图像重建过程中存在的不适定性问题,提出一种稀疏松弛正则化回归模型(SR3)应用于ECT图像重建。采用软阈值迭代法和梯度下降法为SR3模型求解器,向SR3模型中加入L1、L2惩戒项,并设计滤值环节优化解向量。实验结果表明,改进SR3模型算法相比Tikhonov正则化算法、L1正则化算法及原SR3模型算法,重建图像精度明显提高,图像相对误差显著降低,有较好的成像效果。     

调和映射约束下的超分辨率图像重建

针对超分辨率图像重建过程中的正则化约束问题,本文提出采用p(x)调和映射进行正则化重建,根据超分辨率图像观察模型及正则约束,给出相应的能量泛函,并采用动态偏微分方程演化来求解能量泛函.该算法在重建的过程中能够根据图像空间特性自适应地采用不同的p(x)范数进行正则化,在图像的平滑区域采用近似2次范数进行正则化,而在图像的边缘区域采用近似1次范数进行正则化.实验结果均表明该算法不仅能有效地重建图像边缘,而且能有效地改善一次范教约束重建的分片常数效应.     

基于改进低秩稀疏正则化的CFRP电阻抗层析成像算法研究EI北大核心CSCD

碳纤维复合材料(carbon fiber reinforced polymer,CFRP)由于其轻质高强、抗疲劳等优势被广泛应用于航空航天领域。为确保材料使用的安全性,碳纤维复合材料的有效检测尤为重要。近年来,电阻抗层析成像(electrical impedance tomography,EIT)因其低成本、无辐射等优点已成为一种新兴的损伤监测方法并受到了广泛关注。针对电阻抗层析成像逆问题求解具有严重的病态性,提出了一种基于改进低秩稀疏正则化的电阻抗层析成像算法。首先,引入L_(p)伪范数,通过调节p的值来增强解的稀疏性、提高图像重建精度;其次,采用核范数作为解的低秩约束能有效利用先验信息提高重建质量;最后,通过分裂布雷格曼方法求解,增强算法的实时性,使成像速度保持在0.06 s。仿真与试验结果表明,改进低秩稀疏正则化算法能有效改善电极伪影、呈现出更加清晰的损伤细节并且具有较强的鲁棒性、实效性和适用性。     

一种电容层析成像图像重建优化算法

提出一种电学层析成像(ECT)图像重建优化算法。通过将传统正则化算法转化为最小二乘问题进行求解,结合lp范数逼近正则化最小化问题,利用重新加权的方法进行迭代计算。以油-气两相流模型进行仿真及静态实验,将所提出的优化算法与常用的LBP、Landweber迭代及Tikhonov正则化算法进行对比。结果表明,与常用算法相比,采用该优化算法对管道中心物体及多物体分布流型进行图像重建,其图像相对误差均为最低,且重建图像的形状保真度明显提高。     

基于电容层析的LN2-VN2两相流成像经典算法比较研究

针对低温流体液气介电常数接近1的特点,基于八电极电容层析成像(ECT)传感器,通过定量对比图像误差和相关性系数,系统分析了线性反投影算法、Tikhonov正则化算法、Landweber迭代算法、迭代Tikhonov正则化算法、代数重建技术和同步代数重建技术等传统用于室温流体的线性算法,用于LN₂-VN₂两相流的反演图像精度,并指出了各算法优缺点。通过对比水-空气的反演图像,发现LN₂-VN₂反演过程ECT线性化误差较小,从而有更好的反演结果。     

基于卷积稀疏编码的电容层析成像图像重建

针对电容层析成像(ECT)病态性逆问题，提出了一种将卷积稀疏编码模型作为惩罚项嵌入到ECT最小二乘问题的方法，通过预先训练好的滤波器并结合交替方向乘子算法(ADMM)对此模型进行求解，从而完成ECT图像重建。对提出的方法进行了仿真及实验测试，并与LBP、Tikhonov正则化及Landweber迭代算法进行比较。结果表明，提出的方法其重建图像平均相对误差和相关系数分别为0.438 9及0.896 8,均优于其他3种方法，中心物体及多物体分布的重建质量得到显著提升。     

基于自适应步长双参数正则化算法的超声波过程层析成像图像重建

提出了一种新的自适应步长双参数正则化算法,对超声波层析成像系统检测浆体浓度分布进行图像重建。该算法利用转换矩阵将超定解作为先验信息,嵌入到正则化泛函中,避免重建图像被过度平滑,不仅成像速度较快且重建图像具有较高分辨率。仿真实验结果表明,相比于Tikhonov正则化算法以及Landweber算法,自适应步长双参数正则化算法重建图像的相关系数有明显提高并且边界信息更加可靠。     

改进的Tikhonov正则化图像重建算法

Tikhonov正则化法可以解决电容层析成像中图像重建的病态问题,同时能够平衡解的稳定性与精确性,但其有效性和成像质量受到测量数据粗差的影响。改进的Tikhonov正则化法将2范数和M-估计结合,用一个缓慢增长的Cauchy函数代替最小二乘法的平方和函数,提高了估计稳健性和适应性。利用COMSOL和MATLAB软件对方法的有效性进行验证,重建结果表明,改进的Tikhonov正则化法能够有效减少粗差影响,提高重建图像精确度及分辨率。     

基于鲁棒正则化极限学习机的电容层析成像图像重建

电容层析成像图像重建是一个非线性及病态性逆问题。基于此,提出了基于迭代重加权最小二乘法的鲁棒正则化极限学习机(RELM-IRLS)算法的电容层析成像图像重建方法,以油/气两相流为研究对象,通过有限元仿真构建随机分布流型,对RELM-IRLS算法完成训练,并与Landweber迭代算法及极限学习机算法进行对比,RELM-IRLS算法的测试集平均误差相比极限学习机算法减小4.6%。仿真及静态实验结果均表明, RELM-IRLS算法所得重建图像质量得到明显提升,且算法具有良好的泛化性能。     

基于SENet双路径多尺度特征融合的ECT图像重建

针对单一神经网络在电容层析成像图像重建过程中难以捕捉复杂、深层电容向量特征的问题，提出一种基于压缩激励网络(squeeze-and-excitation networks, SENet)双路径多尺度特征融合的电容层析成像图像重建算法。构建多尺度密集深度空洞卷积模块，使模型获得更大的局部感受野的同时可以保持较低计算复杂度，并实现多尺度特征融合，以捕获电容向量的多尺度细节特征，增强模型的表征能力；采用残差神经网络解决深层网络提取特征时出现的退化现象，并添加SENet模块重新标定电容特征张量所属通道对应权重，校准特征响应。形成具有双向特征提取能力的双通道多特征融合的混合模型，以更好的拟合电容张量与介电常数之间的非线性映射关系。试验结果表明，BSFF算法相对于Landweber迭代算法、CNN算法等具有更高的图像重建质量，更好的鲁棒性。     

Efficient reconstruction method for L1 regularization in fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is a promising technique for in vivo small animal imaging. In this paper, the sparsity of the fluorescent sources is considered as the a priori information and is promoted by incorporating L1 regularization. Then a reconstruction algorithm based on stagewise orthogonal matching pursuit is proposed, which treats the FMT problem as the basis pursuit problem. To evaluate this method, we compare it to the iterated-shrinkage-based algorithm with L1 regularization. Numerical simulations and physical experiments show that the proposed method can obtain comparable or even slightly better results. More importantly, the proposed method was at least 2 orders of magnitude faster in these experiments, which makes it a practical reconstruction algorithm.     

Total variation regularization for bioluminescence tomography with the split Bregman method

Regularization methods have been broadly applied to bioluminescence tomography (BLT) to obtain stable solutions, including l2 and l1 regularizations. However, l2 regularization can oversmooth reconstructed images and l1 regularization may sparsify the source distribution, which degrades image quality. In this paper, the use of total variation (TV) regularization in BLT is investigated. Since a nonnegativity constraint can lead to improved image quality, the nonnegative constraint should be considered in BLT. However, TV regularization with a nonnegativity constraint is extremely difficult to solve due to its nondifferentiability and nonlinearity. The aim of this work is to validate the split Bregman method to minimize the TV regularization problem with a nonnegativity constraint for BLT. The performance of split Bregman-resolved TV (SBRTV) based BLT reconstruction algorithm was verified with numerical and in vivo experiments. Experimental results demonstrate that the SBRTV regularization can provide better regularization quality over l2 and l1 regularizations.     

A reconstruction algorithm for electrical impedance tomography based on sparsity regularization

This paper develops a novel sparse reconstruction algorithm for the electrical impedance tomography problem of determining a conductivity parameter from boundary measurements. The sparsity of the ‘inhomogeneity’ with respect to a certain basis is a priori assumed. The proposed approach is motivated by a Tikhonov functional incorporating a sparsity‐promoting ?₁‐penalty term, and it allows us to obtain quantitative results when the assumption is valid. A novel iterative algorithm of soft shrinkage type was proposed. Numerical results for several two‐dimensional problems with both single and multiple convex and nonconvex inclusions were presented to illustrate the features of the proposed algorithm and were compared with one conventional approach based on smoothness regularization. Copyright © 2011 John Wiley & Sons, Ltd.     

Model-resolution based regularization improves near infrared diffuse optical tomography

Diffuse optical tomographic imaging is known to be an ill-posed problem, and a penalty/regularization term is used in image reconstruction (inverse problem) to overcome this limitation. Two schemes that are prevalent are spatially varying (exponential) and constant (standard) regularizations/penalties. A scheme that is also spatially varying but uses the model information is introduced based on the model-resolution matrix. This scheme, along with exponential and standard regularization schemes, is evaluated objectively based on model-resolution and data-resolution matrices. This objective analysis showed that resolution characteristics are better for spatially varying penalties compared to standard regularization; and among spatially varying regularization schemes, the model-resolution based regularization fares well in providing improved data-resolution and model-resolution characteristics. The verification of the same is achieved by performing numerical experiments in reconstructing 1% noisy data involving simple two- and three-dimensional imaging domains.     

An empirical study on compressed sensing MRI using fast composite splitting algorithm and combined sparsifying transforms

The problem of compressed sensing magnetic resonance imaging (CS‐MRI) reconstruction is often formulated as minimizing a linear combination of two terms, including data fidelity and prior regularization. Several prior regularizations can be chosen, including traditional sparsity regularizations such as Total Variance (TV) and wavelet transform, and notably some recently emerging methods such as curvelet and contourlet transforms. Moreover, combinations of multiple different sparsity regularizations are also used in various reconstruction algorithms. Currently, Fast Composite Splitting Algorithm (FCSA) is arguably regarded as one of the most outstanding reconstruction algorithms. This article performs an overall empirical study on using FCSA as the reconstruction algorithm and on different combinations of sparsifying transforms as the regularization terms for CS MRI reconstruction. Experimental results show that (1) the sparsity regularization using the combination of wavelet, curvelet and contourlet yields the best reconstructed image quality but has almost the highest running time in most cases; (2) the combination of wavelet, TV and contourlet can significantly reduce the running time at the cost of slightly compromised reconstruction accuracy; and (3) using contourlet transform solely can also achieve comparable reconstruction accuracy with less running time compared with the combination of TV, wavelet and contourlet. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 302–309, 2015     

Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography

In this paper, a multilevel, hybrid regularization method is presented for fluorescent molecular tomography (FMT) based on the hp-finite element method (hp-FEM) with a continuous wave. The hybrid regularization method combines sparsity regularization and Landweber iterative regularization to improve the stability of the solution of the ill-posed inverse problem. In the first coarse mesh level, considering the fact that the fluorescent probes are sparsely distributed in the entire reconstruction region in most FMT applications, the sparse regularization method is employed to take full advantage of this sparsity. In the subsequent refined mesh levels, since the reconstruction region is reduced and the initial value of the unknown parameters is provided from the previous mesh, these mesh levels seem to be different from the first level. As a result, the Landweber iterative regularization method is applied for reconstruction. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are conducted to evaluate the performance of our method. The reconstructed results show the potential and feasibility of the proposed approach.     

Helmholtz-Type Regularization Method for Permittivity Reconstruction Using Experimental Phantom Data of Electrical Capacitance Tomography

Electrical capacitance tomography (ECT) attempts to image the permittivity distribution of an object by measuring the electrical capacitance between sets of electrodes placed around its periphery. Image reconstruction in ECT is a nonlinear ill-posed inverse problem, and regularization methods are needed to stabilize this inverse problem. The reconstruction of complex shapes (sharp edges) and absolute permittivity values is a more difficult task in ECT, and the commonly used regularization methods in Tikhonov minimization are unable to solve these problems. In the standard Tikhonov regularization method, the regularization matrix has a Laplacian-type structure, which encourages smoothing reconstruction. A Helmholtz-type regularization scheme has been implemented to solve the inverse problem with complicated-shape objects and the absolute permittivity values. The Helmholtz-type regularization has a wavelike property and encourages variations of permittivity. The results from experimental data demonstrate the advantage of the Helmholtz-type regularization for recovering sharp edges over the popular Laplacian-type regularization in the framework of Tikhonov minimization. Furthermore, this paper presents examples of the reconstructed absolute value permittivity map in ECT using experimental phantom data.      

Magnetic resonance imaging reconstruction via non‐convex total variation regularization

Magnetic resonance imaging (MRI) reconstruction model based on total variation (TV) regularization can deal with problems such as incomplete reconstruction, blurred boundary, and residual noise. In this article, a non‐convex isotropic TV regularization reconstruction model is proposed to overcome the drawback. Moreau envelope and minmax‐concave penalty are firstly used to construct the non‐convex regularization of L₂ norm, then it is applied into the TV regularization to construct the sparse reconstruction model. The proposed model can extract the edge contour of the target effectively since it can avoid the underestimation of larger nonzero elements in convex regularization. In addition, the global convexity of the cost function can be guaranteed under certain conditions. Then, an efficient algorithm such as alternating direction method of multipliers is proposed to solve the new cost function. Experimental results show that, compared with several typical image reconstruction methods, the proposed model performs better. Both the relative error and the peak signal‐to‐noise ratio are significantly improved, and the reconstructed images also show better visual effects. The competitive experimental results indicate that the proposed approach is not limited to MRI reconstruction, but it is general enough to be used in other fields with natural images.     

改进的共轭梯度算法的图像重建算法

针对电容层析成像图像重建问题的病态性,在Tikhonov正则化的基础上,以正则化解决方案的规模和给定数据的质量为理论依据,引入一个数学变换,提出了一种新的正则化方法,该方法克服了常规正则化方法扰乱原系统的缺陷。同时,将ECT物理模型进行规范化,并对共轭梯度算法进行改进。仿真实验表明,改进的共轭梯度算法的成像质量高于LBP算法、 Tikhonov正则化算法和共轭梯度算法,并利用相关系数进行了验证。