Wavelet‐based denoising and its impact on analytical SPECT reconstruction with nonuniform attenuation compensation

In single photon emission computed tomography (SPECT), the nonstationary Poisson noise in projection data (sinogram) is a major cause of compromising the quality of reconstructed images. To improve the quality, we must suppress the Poisson noise in the sinogram before or during image reconstruction. However, the conventional space or frequency domain denoising methods will likely remove some information that is very important for accurate image reconstruction, especially for analytical SPECT reconstruction with compensation for nonuniform attenuation. As a time‐frequency analysis tool, wavelet transform has been widely used in the signal and image processing fields and demonstrated its powerful functions in the application of denoising. In this article, we studied the denoising abilities of wavelet‐based denoising method and the impact of the denoising on analytical SPECT reconstruction with nonuniform attenuation. Six popular wavelet‐based denoising methods were tested. The reconstruction results showed that the Revised BivaShrink method with complex wavelet is better than others in analytical SPECT reconstruction with nonuniform attenuation compensation. Meanwhile, we found that the effect of the Anscombe transform for denoising is not significant on the wavelet‐based denoising methods, and the wavelet‐based de‐noise methods can obtain good denoising result even if we do not use Anscombe transform. The wavelet‐based denoising methods are the good choice for analytical SPECT reconstruction with compensation for nonuniform attenuation. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 36–43, 2013     

Filtered backprojection algorithm can outperform iterative maximum likelihood expectation‐maximization algorithm

The iterative maximum‐likelihood expectation‐maximization (ML‐EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML‐EM in certain occasions, when the least‐squared difference from the true image, that is, the least‐squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML‐EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML‐EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML‐EM images. For the noiseless projections, the FBP algorithms outperform the ML‐EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML‐EM algorithm. © 2012 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 22, 114–120, 2012     

基于梯度投影稀疏重建算法的电容层析成像图像重建

为解决两相流中存在中心物体、物体比较小或存在多个物体且相距较近时电容层析成像(ECT)重建图像精度较差的问题,基于稀疏分布的流型其介电常数分布满足稀疏性的先验条件,采用梯度投影稀疏重建(GPSR-BB)算法进行ECT图像重建。仿真及实验测试结果表明:GPSR-BB算法对于流体中小目标以及复杂流型的图像重建质量较好,重建图像的形状保真度高。     

Simultaneous tomographic reconstruction and segmentation with class priors

We consider tomographic imaging problems where the goal is to obtain both a reconstructed image and a corresponding segmentation. A classical approach is to first reconstruct and then segment the image; more recent approaches use a discrete tomography approach where reconstruction and segmentation are combined to produce a reconstruction that is identical to the segmentation. We consider instead a hybrid approach that simultaneously produces both a reconstructed image and segmentation. We incorporate priors about the desired classes of the segmentation through a Hidden Markov Measure Field Model, and we impose a regularization term for the spatial variation of the classes across neighbouring pixels. We also present an efficient implementation of our algorithm based on state-of-the-art numerical optimization algorithms. Simulation experiments with artificial and real data demonstrate that our combined approach can produce better results than the classical two-step approach.     

Image reconstruction with a shift‐variant filtration in circular cone‐beam CT

It is well known that cone‐beam data acquired with a circular orbit are insufficient for exact image reconstruction. Despite this, because a cone‐beam scanning configuration with a circular orbit is easy to implement in practice, it has been widely employed for data acquisition in, e.g., micro‐CT and CT imaging in radiation therapy. The algorithm developed by Feldkamp, Davis, and Kress (FDK) and its modifications, such as the Tent–FDK (T‐FDK) algorithm, have been used for image reconstruction from circular cone‐beam data. In this work, we present an algorithm with spatially shift‐variant filtration for image reconstruction in circular cone‐beam CT. We performed computer‐simulation studies to compare the proposed and existing algorithms. Numerical results in these studies demonstrated that the proposed algorithm has resolution properties comparable to, and noise properties better than, the FDK algorithm. As compared to the T‐FDK algorithm, our proposed algorithm reconstructs images with an improved in‐plane spatial resolution. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 14, 213–221, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20026     

An accelerated multiplicative iterative algorithm in image reconstruction

Based on the ML‐EM (maximum likelihood expectation maximization) algorithm and AWLS (one kind of multiplicative weighted least square) reconstruction, a new algorithm named RMITC (rapid multiplicative iteration with total‐count conservation) is proposed. The new method assumes a higher order correction factor and incorporates a total‐count conservation constraint to obtain better images reconstructed while achieving a higher speed of convergence. Computer simulated phantom data and real positron emission tomography (PET) transmission data were used to compare the new method with other reconstruction algorithms, such as ML‐EM and AWLS. Results demonstrated that the new method is faster and better quantitatively than both ML‐EM and AWLS. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 97–100, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10016     

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.     

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。     

Super resolution in CT

The general framework of super resolution in computed tomography (CT) system is introduced. Two data acquisition ways before or after the reconstruction respectively are described. Three models including the sinogram model, the in‐plane model and the z‐axis model, are addressed to adapt super resolution to CT system. The improved iterative back projection algorithm is used in this work. Experimental results based on simulated data, GE performance phantom scanned by GE LightSpeed VCT system, one patient volunteer scanned by TOSHIBA Aquilion system, and a special experimental apparatus demonstrate that super resolution is effective to improve the resolution of CT images. The sinogram model is suitable for future CT system; the in‐plane model is restricted to some special clinical diagnoses; and the z‐axis model is practicable for current general clinical CT images. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 92–101, 2015     

PET image reconstruction using ANN

The aim of this study is to improve the positron emission tomography (PET) image quality for medical diagnosis. The statistical reconstructions on the maximum a posteriori (MAP) algorithm often results in a blurring effect, which fails to determine the toughness class in the reconstructed image. The development of new reconstruction algorithms for PET is an active field of research. In this article, artificial neural network (ANN) is proposed for replicating the output image, which is generated from the acquired projection data with the corresponding angles using the PET images. This article proposes the advantage of arranging the neural network to stock up the information of the continuous capacity. This reduces the storage space and recuperates as much sequence of the continuous quantity as possible. The performance of image quality parameters using ANN is better when compared with MAP, FBP‐NN (filtered back projection with nearest neighbor interpolation). Thus ANN provides 63% better peak signal to noise ratio (PSNR) when compared with FBP‐NN and 47% better when compared to MAP. Thus, ANN is better than FBP and MAP algorithm, by providing better PSNR. © 2014 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 24, 249–255, 2014     

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     

Neural network-based image reconstruction for positron emission tomography

Positron emission tomography (PET) is one of the key molecular imaging modalities in medicine and biology. Penalized iterative image reconstruction algorithms frequently used in PET are based on maximum-likelihood (ML) and maximum a posterior (MAP) estimation techniques. The ML algorithm produces noisy artifacts whereas the MAP algorithm eliminates noisy artifacts by utilizing availableprior information in the reconstruction process. The MAP-based algorithms fail to determine the density class in the reconstructed image and hence penalize the pixels irrespective of the density class and irrespective of the strength of interaction between the nearest neighbors. A Hebbian neural learning scheme is proposed to model the nature of interpixel interaction to reconstruct artifact-free edge preserving reconstruction. A key motivation of the proposed approach is to avoid oversmoothing across edges that is often the case with MAP algorithms. It is assumed that local correlation plays a significant role in PET image reconstruction, and proper modeling of correlation weight (which defines the strength of interpixel interaction) is essential to generate artifact-free reconstruction. The Hebbian learning-based approach modifies the interaction weight by adding a small correction that is proportional to the product of the input signal (neighborhood pixels) and output signal. Quantitative analysis shows that the Hebbian learning-based adaptive weight adjustment approach is capable of producing better reconstructed images compared with those reconstructed by conventional ML and MAP-based algorithms in PET image reconstruction.     

基于深度信念网络的ECT图像重建算法

为提高图像重建质量,针对电容层析成像技术(ECT)中的电容数据复杂多样且与介电常数呈非线性关系的特点,提出一种基于深度信念网络(DBN)的重建算法,利用DBN的深层非线性网络结构来实现电容值与重建图像灰度值非线性关系.并对DBN进行了改进,将自适应步长(AS)引入到对比散度(CD)算法中,解决固定步长寻找全局最优困难的...     

两相流电容层析成像系统

本文较系统地介绍了电容层析成像系统结构原理,包括抗杂散电容影响的微小检测技术,并行数据采集与处理单元设计以及基于总变差正则化的图像重建算法.与此同时,结合研制的双截面电容成像系统进行试验研究,结果表明该系统不仅可给出实时流型识别,同时能输出表征的特征参数.     

一种基于模型的光学层析图像重建方法

光学层析图像重建是个病态问题,测量误差会在重建过程中被放大,对此,提出一种以广义高斯马尔可夫随机场模型为先验信息的光学层析图像重建方法.重建过程是对目标函数的优化过程,目标函数关于光学参数的梯度计算是算法中的难点,因此,提出一种基于梯度树的梯度计算方法.文中分别给出了吸收系数和散射系数的重建结果,并引入三个指标因子衡量重建图像的质量,进而列出不同重建算法下,重建图像的指标值.最后通过对重建结果和指标因子取值的比较,分析基于模型的重建算法的有效性.     

两相流电容层析成像系统

本文较系统地介绍了电容层析成像系统结构原理,包括抗杂散电容影响的微小检测技术,并行数据采集与处理单元设计以及基于总变差正则化的图像重建算法.与此同时,结合研制的双截面电容成像系统进行试验研究,结果表明该系统不仅可给出实时流型识别,同时能输出表征的特征参数.     

Few‐view image reconstruction combining total variation and a high‐order norm

This work presents a novel computed tomography reconstruction method for few‐view problem based on a compound method. To overcome the disadvantages of total variation (TV) minimization method, we use a high‐order norm coupled within TV and the numerical scheme for our method is given. We use the root mean square error as a referee. The numerical experiments demonstrate that our method achieves better performance than existing reconstruction methods, including filtered back projection, expectation maximization, and TV with projection on convex sets. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 249–255, 2013     

基于BP神经网络的ECT图像重建算法

针对电容层析成像图像重建问题的病态性,利用COMSOL软件建立系统模型,并结合MATLAB实现正问题的求解。依据BP神经网络所具有的理想的非线性映射和联想记忆功能实现了由检测电容值到重建图像灰度值之间的非线性映射,避免了传统算法中对灵敏度矩阵求解的繁琐,克服了因线性化处理所导致的成像精度低的缺点。在MATLAB平台下,采用2种滤波方法进行滤波,对图像增强修复,提高了图像质量。     

Sparse‐view statistical iterative head CT image reconstruction via joint regularization

It is a significant challenge to accurately reconstruct medical computed tomography (CT) images with important details and features. Reconstructed images always suffer from noise and artifact pollution because the acquired projection data may be insufficient or undersampled. In reality, some “isolated noise points” (similar to impulse noise) always exist in low‐dose CT projection measurements. Statistical iterative reconstruction (SIR) methods have shown greater potential to significantly reduce quantum noise but still maintain the image quality of reconstructions than the conventional filtered back‐projection (FBP) reconstruction algorithm. Although the typical total variation‐based SIR algorithms can obtain reconstructed images of relatively good quality, noticeable patchy artifacts are still unavoidable. To address such problems as impulse‐noise pollution and patchy‐artifact pollution, this work, for the first time, proposes a joint regularization constrained SIR algorithm for sparse‐view CT image reconstruction, named “SIR‐JR” for simplicity. The new joint regularization consists of two components: total generalized variation, which could process images with many directional features and yield high‐order smoothness, and the neighborhood median prior, which is a powerful filtering tool for impulse noise. Subsequently, a new alternating iterative algorithm is utilized to solve the objective function. Experiments on different head phantoms show that the obtained reconstruction images are of superior quality and that the presented method is feasible and effective.     

Kalman滤波在电容层析成像图像重建中的应用

利用Kalman滤波算法进行电容层析成像图像重建,通过不断更新测量信息提高重建图像质量。在滤波初始,需要确定重建图像灰度及估计误差方差矩阵的初值。为研究不同初值组合对重建图像质量的影响,选择3流型进行了仿真实验,获得了最佳的初值组合,并在电容层析成像实验装置上进行了静态测试,实验结果表明,与Landweber算法相比,使用最佳初值组合的Kalman滤波算法可获得更为接近真实分布的重建图像。