Neural network reconstruction of single-photon emission computed tomography images

An artificial neural network (ANN) trained on high-quality medical tomograms or phantom images may be able to learn the planar data-to-tomographic image relationship with very high precision. As a result, a properly trained ANN can produce comparably accurate image reconstruction without the high computational cost inherent in some traditional reconstruction techniques. We have previously shown that a standard backpropagation neural network can be trained to reconstruct sections of single photon emission computed tomography (SPECT) images based on the planar image projections as inputs. In this study, we present a method of deriving activation functions for a backpropagation ANN that make it readily trainable for full SPECT image reconstruction. The activation functions used for this work are based on the estimated probability density functions (PDFs) of the ANN training set data. The statistically tailored ANN and the standard sigmoidal backpropagation ANN methods are compared both in terms of their trainability and generalization ability. The results presented show that a statistically tailored ANN can reconstruct novel tomographic images of a quality comparable with that of the images used to train the network. Ultimately, an adequately trained ANN should be able to properly compensate for physical photon transport effects, background noise, and artifacts while reconstructing the tomographic image.     

Artificial neural network Radon inversion for image reconstruction

Image reconstruction techniques are essential to computer tomography. Algorithms such as filtered backprojection (FBP) or algebraic techniques are most frequently used. This paper presents an attempt to apply a feed-forward back-propagation supervised artificial neural network (BPN) to tomographic image reconstruction, specifically to positron emission tomography (PET). The main result is that the network trained with Gaussian test images proved to be successful at reconstructing images from projection sets derived from arbitrary objects. Additional results relate to the design of the network and the full width at half maximum (FWHM) of the Gaussians in the training sets. First, the optimal number of nodes in the middle layer is about an order of magnitude less than the number of input or output nodes. Second, the number of iterations required to achieve a required training set tolerance appeared to decrease exponentially with the number of nodes in the middle layer. Finally, for training sets containing Gaussians of a single width, the optimal accuracy of reconstructing the control set is obtained with a FWHM of three pixels. Intended to explore feasibility, the BPN presented in the following does not provide reconstruction accuracy adequate for immediate application to PET. However, the trained network does reconstruct general images independent of the data with which it was trained. Proposed in the concluding section are several possible refinements that should permit the development of a network capable of fast reconstruction of three-dimensional images from the discrete, noisy projection data characteristic of PET.     

Arterial spin labeling MR image denoising and reconstruction using unsupervised deep learning

Arterial spin labeling (ASL) imaging is a powerful magnetic resonance imaging technique that allows to quantitatively measure blood perfusion non-invasively, which has great potential for assessing tissue viability in various clinical settings. However, the clinical applications of ASL are currently limited by its low signal-to-noise ratio (SNR), limited spatial resolution, and long imaging time. In this work, we propose an unsupervised deep learning-based image denoising and reconstruction framework to improve the SNR and accelerate the imaging speed of high resolution ASL imaging. The unique feature of the proposed framework is that it does not require any prior training pairs but only the subject's own anatomical prior, such as T1-weighted images, as network input. The neural network was trained from scratch in the denoising or reconstruction process, with noisy images or sparely sampled k-space data as training labels. Performance of the proposed method was evaluated using in vivo experiment data obtained from 3 healthy subjects on a 3T MR scanner, using ASL images acquired with 44-min acquisition time as the ground truth. Both qualitative and quantitative analyses demonstrate the superior performance of the proposed txtc framework over the reference methods. In summary, our proposed unsupervised deep learning-based denoising and reconstruction framework can improve the image quality and accelerate the imaging speed of ASL imaging.     

Development and evaluation of an exact fan-beam reconstruction algorithm using an equal weighting scheme via locally compensated filtered backprojection (LCFBP)

A novel exact fan-beam image reconstruction formula is presented and validated using both phantom data and clinical data. This algorithm takes the form of the standard ramp filtered backprojection (FBP) algorithm plus local compensation terms. This algorithm will be referred to as a locally compensated filtered backprojection (LCFBP). An equal weighting scheme is utilized in this algorithm in order to properly account for redundantly measured projection data. The algorithm has the desirable property of maintaining a mathematically exact result for: the full scan mode (2pi), the short scan mode (pi+ full fan angle), and the supershort scan mode [less than (pi+ full fan angle)]. Another desirable feature of this algorithm is that it is derivative-free. This feature is beneficial in preserving the spatial resolution of the reconstructed images. The third feature is that an equal weighting scheme has been utilized in the algorithm, thus the new algorithm has better noise properties than the standard filtered backprojection image reconstruction with a smooth weighting function. Both phantom data and clinical data were utilized to validate the algorithm and demonstrate the superior noise properties of the new algorithm.     

An improved ordered subsets expectation maximization positron emission computerized tomography reconstruction

Ordered subsets expectation maximization (OS-EM) reconstruction method is usually used in positron emission tomography (PET). But it has some disadvantage such as long computation time and bad reconstruction quality. Filtered back projection (FBP), that has many advantages such as simple structure and short reconstruction time, is firstly introduced into the initialization stage of the OS-EM to fast the reconstruction process. Then, the smoothness method is applied after the OS-EM algorithm to improve the reconstruction speed and quality. The reconstructed images are compared for both the simulated phantom data and the brain magnetic resonance imaging data. The improved OS-EM is shown to be more feasible than the standard OS-EM within the same iteration steps and in higher signal noise ratio (SNR) condition.     

Fan-beam filtered-backprojection reconstruction without backprojection weight

In this paper, we address the problem of two-dimensional image reconstruction from fan-beam data acquired along a full 2pi scan. Conventional approaches that follow the filtered-backprojection (FBP) structure require a weighted backprojection with the weight depending on the point to be reconstructed and also on the source position; this weight appears only in the case of divergent beam geometries. Compared to reconstruction from parallel-beam data, the backprojection weight implies an increase in computational effort and is also thought to have some negative impacts on noise properties of the reconstructed images. We demonstrate here that direct FBP reconstruction from full-scan fan-beam data is possible with no backprojection weight. Using computer-simulated, realistic fan-beam data, we compared our novel FBP formula with no backprojection weight to the use of an FBP formula based on equal weighting of all data. Comparisons in terms of signal-to-noise ratio, spatial resolution and computational efficiency are presented. These studies show that the formula we suggest yields images with a reduced noise level, at almost identical spatial resolution. This effect increases quickly with the distance from the center of the field of view, from 0% at the center to 20% less noise at 20 cm, and to 40% less noise at 25 cm. Furthermore, the suggested method is computationally less demanding and reduces computation time with a gain that was found to vary between 12% and 43% on the computers used for evaluation.     

Dual energy CT using slow kVp switching acquisition and prior image constrained compressed sensing

Dual energy computed tomography (DECT) is currently a subject of extensive investigation. DECT is currently implemented using either a dual source scanner with high and low kVp data acquired from separate sources or a single source scanner with both high and low kVp data acquired in an alternating manner. Both methods require dedicated hardware to enable data acquisition and image reconstruction for DECT. In this paper, we present a method to enable DECT using a single x-ray source with a slow kVp switching data acquisition. The enabling reconstruction technique allowing for the reduction in slew rate is the prior image constrained compressed sensing (PICCS) algorithm. When a slow kVp switching data acquisition method is used, the projection data with high and low kVp values are undersampled and the conventional filtered backprojection (FBP) image reconstruction does not enable streaking artifact-free images for material decomposition in DECT. In this paper, all of the acquired high and low kVp projection data were used to generate a prior image using the conventional FBP method. The PICCS algorithm was then used to reconstruct both high and low kVp images to enable material decomposition in the image domain. Both numerical simulations and physical phantom experimental studies were conducted to validate the proposed DECT scheme. The results demonstrate that a slew rate corresponding to 123 views at high and low kVp (high and low kVp values used for dual energy decomposition) is sufficient for the PICCS-based DECT method. In contrast, the slew rate should be high enough to obtain over 500 projections at each kVp for artifact-free reconstruction using an FBP-based DECT method.     

基于深度学习单投影的CT断层成像三维重建

【摘要】目的:提出一种基于深度学习的计算机断层扫描（CT）单视图断层成像三维（3D）重建方法,在减少数据采集量和降低成像剂量的情况下对不同患者进行CT图像的3D重建。方法:对不同患者的CT图像进行数据增强和模拟生成对应的数字重建放射影像（DRR）,并进行数据归一化操作。利用预处理后的数据通过卷积神经网络训练出一个普适于不同患者的神经网络模型。将训练好的神经网络模型部署在测试数据集上,使用平均绝对误差（MAE）、均方根误差（RMSE）、结构相似性（SSIM）和峰值信噪比（PSNR）对重建结果进行评估。结果:定性和定量分析的结果表明,该方法可以使用不同患者的单张2D图像分别重建出质量较高的3D CT图像,MAE、RMSE、SSIM和PSNR分别为0.006、0.079、0.982、38.424 dB。此外,相比特定于单个患者的情况,该方法可以大幅度提高重建速度并节省70%的模型训练时间。结论:构建的神经网络模型可通过不同患者的2D单视图重建出相应患者的3D CT图像。因此,本研究对简化临床成像设备和放射治疗当中的图像引导具有重要作用。     

Suppression of intensity transition artifacts in statistical x-ray computer tomography reconstruction through radon inversion initialization

Statistical reconstruction (SR) methods provide a general and flexible framework for obtaining tomographic images from projections. For several applications SR has been shown to outperform analytical algorithms in terms of resolution-noise trade-off achieved in the reconstructions. A disadvantage of SR is the long computational time required to obtain the reconstructions, in particular when large data sets characteristic for x-ray computer tomography (CT) are involved. As was shown recently, by combining statistical methods with block iterative acceleration schemes [e.g., like in the ordered subsets convex (OSC) algorithm], the reconstruction time for x-ray CT applications can be reduced by about two orders of magnitude. There are, however, some factors lengthening the reconstruction process that hamper both accelerated and standard statistical algorithms to similar degree. In this simulation study based on monoenergetic and scatter-free projection data, we demonstrate that one of these factors is the extremely high number of iterations needed to remove artifacts that can appear around high-contrast structures. We also show (using the OSC method) that these artifacts can be adequately suppressed if statistical reconstruction is initialized with images generated by means of Radon inversion algorithms like filtered back projection (FBP). This allows the reconstruction time to be shortened by even as much as one order of magnitude. Although the initialization of the statistical algorithm with FBP image introduces some additional noise into the first iteration of OSC reconstruction, the resolution-noise trade-off and the contrast-to-noise ratio of final images are not markedly compromised.     

Massive training artificial neural network (MTANN) for reduction of false positives in computerized detection of lung nodules in low-dose computed tomography

In this study, we investigated a pattern-recognition technique based on an artificial neural network (ANN), which is called a massive training artificial neural network (MTANN), for reduction of false positives in computerized detection of lung nodules in low-dose computed tomography (CT) images. The MTANN consists of a modified multilayer ANN, which is capable of operating on image data directly. The MTANN is trained by use of a large number of subregions extracted from input images together with the teacher images containing the distribution for the "likelihood of being a nodule." The output image is obtained by scanning an input image with the MTANN. The distinction between a nodule and a non-nodule is made by use of a score which is defined from the output image of the trained MTANN. In order to eliminate various types of non-nodules, we extended the capability of a single MTANN, and developed a multiple MTANN (Multi-MTANN). The Multi-MTANN consists of plural MTANNs that are arranged in parallel. Each MTANN is trained by using the same nodules, but with a different type of non-nodule. Each MTANN acts as an expert for a specific type of non-nodule, e.g., five different MTANNs were trained to distinguish nodules from various-sized vessels; four other MTANNs were applied to eliminate some other opacities. The outputs of the MTANNs were combined by using the logical AND operation such that each of the trained MTANNs eliminated none of the nodules, but removed the specific type of non-nodule with which the MTANN was trained, and thus removed various types of non-nodules. The Multi-MTANN consisting of nine MTANNs was trained with 10 typical nodules and 10 non-nodules representing each of nine different non-nodule types (90 training non-nodules overall) in a training set. The trained Multi-MTANN was applied to the reduction of false positives reported by our current computerized scheme for lung nodule detection based on a database of 63 low-dose CT scans (1765 sections), which contained 71 confirmed nodules including 66 biopsy-confirmed primary cancers, from a lung cancer screening program. The Multi-MTANN was applied to 58 true positives (nodules from 54 patients) and 1726 false positives (non-nodules) reported by our current scheme in a validation test; these were different from the training set. The results indicated that 83% (1424/1726) of non-nodules were removed with a reduction of one true positive (nodule), i.e., a classification sensitivity of 98.3% (57 of 58 nodules). By using the Multi-MTANN, the false-positive rate of our current scheme was improved from 0.98 to 0.18 false positives per section (from 27.4 to 4.8 per patient) at an overall sensitivity of 80.3% (57/71).     

Analytical reconstruction of deconvolved Fourier rebinned PET sinograms

Fully 3D PET data are often rebinned into 2D data sets in order to avoid computationally intensive fully 3D reconstruction. Then, conventional 2D reconstruction techniques are employed to obtain images from the rebinned data. In a common scenario, 2D filtered back projection (FBP) is applied to Fourier rebinned (FORE) data. This approach is suboptimal because FBP is based on an idealized mathematical model of the data and cannot account for the statistical structure of data and noise. FORE data contain some blur in all three dimensions in comparison to conventional 2D PET data. In this work, we propose methods for approximating this blur in the sinogram domain due to FORE through its point spread function (PSF). We also explore simple methods for deconvolving the rebinned data with this PSF to restore it to a more ideal state prior to FBP. Our results show that deconvolution of the approximate transaxial PSF yields no improvement. When low image noise levels are required for detection tasks, the deconvolution of the axial PSF does not provide adequate resolution or quantitative benefits to justify its application. When accurate quantitation is required and higher noise levels are acceptable, the deconvolution of the axial PSF leads to considerable gains (30%) in accuracy over conventional FORE+FBP at matched noise levels.     

Analytic image reconstruction in local phase-contrast tomography

Phase-contrast tomography is a non-interferometric imaging technique for reconstructing the refractive index distribution of a weakly absorbing object from a set of tomographic projection measurements. In many practical situations, the spatial resolution of the reconstructed image can be increased by minimizing the field of view (FOV) of the imaging system. When the object of interest is larger than the FOV, the measured projections are truncated and one is faced with a local tomography reconstruction problem. In this work, we analytically and numerically investigate the problem of reconstructing tomographic images from truncated phase-contrast projection data. A simple backprojection algorithm for reconstructing object discontinuities from truncated phase-contrast projection data is proposed and investigated that involves no explicit filtering of the projection data. We also investigate the use of the filtered backprojection algorithm and a local tomography reconstruction algorithm developed for absorption CT. These reconstruction algorithms are implemented and numerically investigated to corroborate our theoretical assertions.     

基于投影矩阵广义逆的CT重建迭代算法

目的在CT检查时,有限角度投影和稀疏矩阵投影能够减少X射线的剂量,然而这会导致投影数据不足,给图像重建带来一定的困难。为了克服这一难题得到较好的重建图像,本文提出一种基于计算投影矩阵广义逆的CT迭代重建算法。方法该算法在计算过程中,将重建图像表示为投影矩阵以及其广义逆的乘积。首先使用一阶迭代计算广义逆矩阵,但是由于投影矩阵和其广义逆矩阵都比较大,在迭代过程中以投影和滤波反投影代替。然后通过不同的算法分别对平行束投影、有限角度投影、稀疏矩阵投影的数据进行重建,并对重建结果的均方差、通用图像质量指标以及图像互信息进行比较。结果本文提出的方法重建出图像的均方差、通用图像质量指标和图像互信息更优,而且重建时间较短。结论该方法能够在没有未知图像先验结构信息和伪影猜想的情况下有效地提高重建图像的质量,而且该算法不需要计算投影过程,重建过程简单易行。     

基于双层字典学习的低剂量CT图像重建算法

目的低剂量投影条件下的CT图像重建。方法采用双层K-奇异值分解(K-singular value decomposition,K-SVD)字典训练的学习方法进行图像的超分辨率重建。字典学习方法中采用KSVD算法,稀疏编码采用正交匹配追踪(orthogonal matching pursuit,OMP)算法。该算法首先利用训练库进行第一层字典训练,然后利用第一层训练的字典对低分辨率图像进行重建。进而将重建图像作为第二层待重建图像的输入,这样使得第二层输入图像含有较多的高频细节信息,因此能在重构的过程中恢复更多的细节信息,让高分辨率重构图像达到较好的效果。结果双层字典重建效果明显优于KSVD算法,重建图像更接近于原始高分辨率CT图像。结论本研究对双层字典训练学习的框架进行反迭代投影的全局优化改进,改善了图像的重建质量。     

Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector

In this paper, we present a new algorithm designed for a specific data truncation problem in fan-beam CT. We consider a scanning configuration in which the fan-beam projection data are acquired from an asymmetrically positioned half-sized detector. Namely, the asymmetric detector only covers one half of the scanning field of view. Thus, the acquired fan-beam projection data are truncated at every view angle. If an explicit data rebinning process is not invoked, this data acquisition configuration will reek havoc on many known fan-beam image reconstruction schemes including the standard filtered backprojection (FBP) algorithm and the super-short-scan FBP reconstruction algorithms. However, we demonstrate that a recently developed fan-beam image reconstruction algorithm which reconstructs an image via filtering a backprojection image of differentiated projection data (FBPD) survives the above fan-beam data truncation problem. Namely, we may exactly reconstruct the whole image object using the truncated data acquired in a full scan mode (2pi angular range). We may also exactly reconstruct a small region of interest (ROI) using the truncated projection data acquired in a short-scan mode (less than 2pi angular range). The most important characteristic of the proposed reconstruction scheme is that an explicit data rebinning process is not introduced. Numerical simulations were conducted to validate the new reconstruction algorithm.     

A hierarchical neural network algorithm for robust and automatic windowing of MR images

A novel hierarchical neural network based algorithm for automatic adjustment of display window width and center for a wide range of magnetic resonance (MR) images is presented in this paper. The algorithm consists of a feature generator utilizing both wavelet histogram and compact spatial statistical information computed from a MR image, a competitive layer based neural network for clustering MR images into different subclasses, two pairs of a radial basis function (RBF) network and a bi-modal linear estimator for each subclass, as well as a data fusion process using estimates from both estimators to compute the final display parameters. Both estimators can adapt to new kinds of MR images simply by training them with those images, which make the algorithm adaptive and extendable. The RBF based estimator performs very well for images that are similar to those in the training data set. The bi-modal linear estimator provides reasonable estimations for a wide range of images that may not be included in the training data set. The data fusion step makes the final estimation of the display parameters accurate for trained images and robust for the unknown images. The algorithm has been tested on a wide range of MR images and has shown satisfactory results.     

Evaluation of Apparent Noise on CT Images Using Moving Average Filters

This study aims to devise a simple method for evaluating the magnitude of texture noise (apparent noise) observed on computed tomography (CT) images scanned at a low radiation dose and reconstructed using iterative reconstruction (IR) and deep learning reconstruction (DLR) algorithms, and to evaluate the apparent noise in CT images reconstructed using the filtered back projection (FBP), IR, and two types of DLR (AiCE Body and AiCE Body Sharp) algorithms. We set a square region of interest (ROI) on CT images of standard- and obese-sized low-contrast phantoms, slid different-sized moving average filters in the ROI vertically and horizontally in steps of 1 pixel, and calculated the standard deviation (SD) of the mean CT values for each filter size. The SD of the mean CT values was fitted with a curve inversely proportional to the filter size, and an apparent noise index was determined from the curve-fitting formula. The apparent noise index of AiCE Body Sharp images for a given mAs value was approximately 58, 23, and 18% lower than that of the FBP, AIDR 3D, and AiCE Body images, respectively. The apparent noise index was considered to reflect noise power spectrum values at lower spatial frequency. Moreover, the apparent noise index was inversely proportional to the square roots of the mAs values. Thus, the apparent noise index could be a useful indicator to quantify and compare texture noise on CT images obtained with different scan parameters and reconstruction algorithms.

     

CT快速二维反投影算法

CT图像重建过程中，标准的二维反投影运算计算量为D(N^3)。本研究提出一种快速二维反投影算法，其计算量仅为D(N^2log2^N)。该快速算法可以并行实现，处理器阵列规模为D(N^2)时，计算量为D(log2^x)。本研究还分析得到快速算法的误差上界，并提出一种改进的快速二维反投影算法以获得更高的计算精度。最后，对算法进行了仿真实验。理论分析及仿真实验结果都表明，本研究的二维反投影算法在CT图像重建过程中有着更高的计算效率，并且具有良好的计算精度。     

图像域迭代重建算法对腹部CT平扫图像质量和辐射剂量的影响

目的:探讨图像域迭代重建算法对腹部CT平扫图像质量及辐射剂量的影响。 方法:以辽阳市中心医院2017年1月~2018年4月行腹部CT平扫的150例患者为研究对象,依据就诊先后顺序随机将其分为观察组与对照组,各75例。均行自动毫安控制技术扫描,管电压均为130 kV。观察组预设图像质量参考毫安秒150 mAs,行图像域迭代重建算法重建;对照组预设图像质量参考毫安秒250 mAs,行滤波反投影重组。通过CT值、图像噪声SD、图像信噪比、对比噪声比评价两组图像客观质量,并行图像质量主观评价,记录两组CT剂量容积指数。 结果:观察组肝脏、脾脏的图像噪声SD均显著低于对照组,图像信噪比均显著高于对照组,差异有统计学意义（P<0.05）;CT值、对比噪声比、主观整体质量评分两组比较差异均无统计学意义（P>0.05）;观察组CT剂量容积指数为（10.02±2.85） mGy,显著低于对照组的（15.68±4.36） mGy,差异有统计学意义（P<0.05）。 结论:图像域迭代重建算法不仅能保证腹部CT平扫图像质量,而且能有效减少辐射剂量。     

Noise and signal decoupling in maximum-likelihood reconstructions and Metz filters for PET brain images

Images reconstructed with the maximum-likelihood-by-expectation-maximization (ML) algorithm have lower noise in some regions, particularly low count areas, compared with images reconstructed with filtered backprojection (FBP). The use of statistically correct noise model coupled with the positivity constraint in the ML algorithm provides this noise improvement, but whether this model confers a general advantage for ML over FBP with no noise model and any reconstruction filter, is unclear. We have studied the quantitative impact of the correct noise model in the ML algorithm applied to simulated and real PET fluoro-deoxyglucose (FDG) brain images, given a simplified but accurate reconstruction model with spatially invariant resolution. For FBP reconstruction, several Metz filters were chosen and images with different resolution were obtained depending on the order (1-400) of the Metz filters. Comparisons were made based on the mean Fourier spectra of the projection amplitudes, the noise-power spectra, and the mean region-of-interest signal and noise behaviour in the images. For images with resolution recovery beyond the intrinsic detector resolution, the noise increased significantly for FBP compared with ML. This indicates that in the process of signal recovery using ML, the noise is decoupled from the signal. Such noise decoupling is not possible for FBP. However, for image resolution equivalent to or less than the intrinsic detector resolution, FBP with Metz filters of various orders can achieve a performance similar to ML. The significance of the noise decoupling advantage in ML is dependent on the reconstructed image resolution required for specific imaging tasks.