一种基于时空变换和压缩感知的磁共振螺旋采样的图像重建算法

螺旋采样磁共振快速成像在功能性成像、并行成像和动态成像等领域发挥着越来越重要的作用.螺旋采样图像重建的传统算法是用核函数将螺旋状分布的k空间数据插值到均匀网格中,再利用傅里叶变换和最小二乘法进行重建.但是基于网格化的算法对核函数过于依赖,在网格化过程中产生难以避免的误差.该文提出了基于时空变换和压缩感知的l1范数的最优化模型和重建算法.时空变换矩阵描述了空间上的磁共振图像与采集到的时域信号间的关系,使得算法直接使用采集到的数据作为保真约束项,避免了网格化过程产生的误差.此外,基于图像处理单元的并行计算被用来提高时空变换矩阵的运算速度,使得算法具有较强的应用价值.     

激光共焦扫描显微镜三维数据场截面图像重建

提出利用插值技术实现离散三维数据场重采样的算法，并利用计算机图形学技术显示重建图像。     

小波双线性插值迭代算法应用于光学遥感图像

分析了小波双线性插值中高频外推阈值门限与重建图像峰值信噪比的变化关系,提出了峰值信噪比最大小波双线性插值迭代算法.提出的算法能够自动搜索到峰值信噪比最大的高频外推最佳阈值门限,实现了在不破坏光学遥感图像原始信息的情况下,提高图像的空间分辨率,有利于对图像的细节信息进行观察分析.实验结果表明,该算法重建图像的峰值信噪比比双线性插值和全小波插值重建图像的峰值信噪比高5.5 dB和2.5 dB,重建图像的熵增加到原图像的1.3倍.     

一种TDI CCD亚像元图像合成方法

通过分析TDI CCD亚像元相机输出数据的空间和频谱特点,设计了亚像元插值算法,由相机输出的两幅原始图像经过插值融合处理得到一幅比原图像分辨率高的图像.仿真结果表明,该算法较其它算法得到的高分辨率图像的效果更佳,融合之后的图像比原图像分辨率提高至少1.4倍.     

一种保持二阶精度的反距离加权空间插值算法

针对传统反距离加权（IDW）插值精度较低的缺陷,发展一种高精度插值算法.该插值算法采用迭代亏量校正技术（IDeC）对一次反距离加权插值结果进行修正,通过有限次迭代,理论上将计算精度提高至二阶.在基于结构化网格、非结构化网格的数值验证中,该插值算法的计算精度均保持在二阶左右.应用该算法针对二维圆形和三维球形界面重构时,算法提高了重构界面的光滑度,且计算精度保持为二阶.双层网格插值实验中,算法将速度和压力的绝对误差降低45%以上,得到的压力等值线更接近于初始场.     

一类基于ENO插值的守恒重映算法

在大变形流体力学问题的数值模拟中,常常会涉及到计算网格的重分.基于不同网格的物理量传递便是所谓的重映技术.基于ENO插值的思想,发展了一类适用于任意网格的ENO守恒重映算法,并给出了数值结果.     

数据插值对正电子发射断层成像设备的图像重建影响的研究

正电子发射断层扫描(positron emission computed tomography, PET)是核医学领域最先进的临床检查影像技术. PET技术是目前临床上用于诊断和指导治疗肿瘤的最佳手段之一. 正电子发射断层成像设备探测器采集到的数据需要进行数据处理, 把原始数据转换成正弦图形式的数据才能用于图像重建. 平行束断层重建和扇形束图像重建是图像重建的两种方法, 分别对应平行束和扇形束形式的数据处理方法. 对原始数据的操作不可避免地破坏了原始数据的完整性. 现今, 正电子发射断层设备在重建过程中普遍采用平行束重建的方法. 平行束的数据分离会对PET数据进行插值操作, 扇形束的数据分离不会对PET数据进行插值操作. 本文通过对比平行束图像重建和扇形束图像重建结果, 研究了数据插值对PET图像重建结果的影响. 关键词： 正电子发射计算机断层扫描 数据插值 图像重建 原始数据     

基于快速小波分形插值的声纳图像缩放算法

本文讨论主动图像声纳的图像结果显示问题,主要介绍一种基于快速小波分形插值的实时声纳图像缩放算法。并通过对合成孔径声纳图像数据进行算法比较,发现此算法比通用的图像插值算法,如双线性插值和双三次样条插值等,具有更好的性能。由于可以分块并行实现,因此本算法易于应用于实时图像声纳工程中。     

基于Gadgetron平台的多GPU分布式磁共振图像重建

为了满足磁共振成像（MRI）临床扫描的需求,磁共振图像重建算法的开发一直在不断进行.目前广泛使用的算法实现方式是利用中央处理器（CPU）对磁共振扫描数据进行数学变换得到图像,随着算法复杂度的提升,计算性能问题逐渐显露.利用CPU在大数据量下执行复杂算法时,计算并行性的缺失以及运算中产生的海量数据的存储负荷会导致计算变得极为缓慢,使得一些算法因为重建时间过长,在临床上面临难以推广的问题,也制约了基础研究中新算法的研发.本文设计并实现了一种新的重建算法执行方式,利用Gadgetron磁共振软件重建平台在多核CPU基础上搭载多块图形处理器（GPU）,将磁共振图像重建以分布式并行计算方式实现,并以重建耗时较长的3D径向数据采集Stack of Star（SOS）的图像重建为实例,展示这种重建的实现方法能以相对低廉的硬件成本极大提升重建的速度.     

炉膛三维温度场重建中Tikhonov正则化和截断奇异值分解算法比较

在煤粉锅炉诊断中火焰辐射能图像扮演着越来越重要的角色, 通过电荷耦合器件(CCD)获得的辐射能图像可以重建出炉内火焰三维温度场, CCD 用于获取视场角内的辐射能图像. 温度场重建的矩阵方程是一个严重病态的方程, 本文使用两种算法(Tikhonov正则化算法和截断奇异值分解(TSVD)算法)来重建温度场. 应用广义交叉检验算法来选取正确的正则化参数. 数值模拟的环境为一个10 m×10 m×10 m的三维炉膛, 系统被划分为10×10×10的1000个网格, 每个网格单元都是边长为1 m的立方体. 在正问题求解所得到的CCD接受信号基础上加上不同随机误差以模拟测量时的CCD接受信号. 研究两种算法重建后的温度重建误差、两者的重建时间, 以及最高温度的重建效果. 初步的研究结果显示, 一般情况下基于Tikhonov算法重建的温度场比基于TSVD算法重建的温度场误差要小, 计算所需时间短, 最高温度重建更准确.     

On NUFFT-based gridding for non-Cartesian MRI

For MRI with non-Cartesian sampling, the conventional approach to reconstructing images is to use the gridding method with a Kaiser-Bessel (KB) interpolation kernel. Recently, Sha et al. [L. Sha, H. Guo, A.W. Song, An improved gridding method for spiral MRI using nonuniform fast Fourier transform, J. Magn. Reson. 162(2) (2003) 250-258] proposed an alternative method based on a nonuniform FFT (NUFFT) with least-squares (LS) design of the interpolation coefficients. They described this LS_NUFFT method as shift variant and reported that it yielded smaller reconstruction approximation errors than the conventional shift-invariant KB approach. This paper analyzes the LS_NUFFT approach in detail. We show that when one accounts for a certain linear phase factor, the core of the LS_NUFFT interpolator is in fact real and shift invariant. Furthermore, we find that the KB approach yields smaller errors than the original LS_NUFFT approach. We show that optimizing certain scaling factors can lead to a somewhat improved LS_NUFFT approach, but the high computation cost seems to outweigh the modest reduction in reconstruction error. We conclude that the standard KB approach, with appropriate parameters as described in the literature, remains the practical method of choice for gridding reconstruction in MRI.     

An improved gridding method for spiral MRI using nonuniform fast Fourier transform

The algorithm of Liu and Nguyen [IEEE Microw. Guided Wave Lett. 8 (1) (1998) 18; SIAM J. Sci. Comput. 21 (1) (1999) 283] for nonuniform fast Fourier transform (NUFFT) has been extended to two dimensions to reconstruct images using spiral MRI. The new gridding method, called LS_NUFFT, minimizes the reconstruction approximation error in the Least Square sense by generated convolution kernels that fit for the spiral k-space trajectories. For analytical comparison, the LS_NUFFT has been fitted into a consistent framework with the conventional gridding methods using Kaiser-Bessel gridding and a recently proposed generalized FFT (GFFT) approach. Experimental comparison was made by assessing the performance of the LS_NUFFT with that of the standard direct summation method and the Kaiser-Bessel gridding method, using both digital phantom data and in vivo experimental data. Because of the explicitly optimized convolution kernel in LS_NUFFT, reconstruction results showed that the LS_NUFFT yields smaller reconstruction approximation error than the Kaiser-Bessel gridding method, but with the same computation complexity.     

改进的插值法用于IIM影像条带噪声去除

摘 要：针对嫦娥一号(CE-1)干涉成像光谱仪(IIM)影像中的条带噪声,应用常用的频域滤波方法和线性插值法进行了IIM条带去除试验,并提出结合了三阶插值的改进线性插值方法。对噪声点定位后,根据图像中噪声点上下行相应点的数值差别是否超过预设阈值,确定是采用线性插值还是三阶插值算法,修正噪声点像素值。实验结果的均值和标准偏差以及图像质量因子(IQ因子)的比较表明：改进的方法IQ值达到13.9081,而线性插值算法为9.8428,改进的线性插值方法在去除IIM影像条带噪声方面明显优于线性插值方法。     

双树小波变换与小波树稀疏联合的低场CS-MRI算法

压缩感知理论常用在磁共振快速成像上,仅采样少量的K空间数据即可重建出高质量的磁共振图像.压缩感知磁共振成像技术的原理是将磁共振图像重建问题建模成一个包含数据保真项、稀疏先验项和全变分项的线性组合最小化问题,显著减少磁共振扫描时间.稀疏表示是压缩感知理论的一个关键假设,重建结果很大程度上依赖于稀疏变换.本文将双树复小波变换和小波树稀疏联合作为压缩感知磁共振成像中的稀疏变换,提出了基于双树小波变换和小波树稀疏的压缩感知低场磁共振图像重建算法.实验表明,本文所提算法可以在某些磁共振图像客观评价指标中表现出一定的优势.     

基于稀疏重建的磁共振图像尖峰噪声消除方法

磁共振图像K空间中的尖峰噪声会严重影响图像质量.该文在磁共振图像压缩感知的共轭梯度重建法的基础上,提出一种新的利用磁共振图像稀疏性进行尖峰噪声修复的方法.传统的共轭梯度重建是通过小波域迭代进行的,对于K空间的尖峰噪声的消除不是最适合.首先提出压缩感知的K空间重建算法,该算法与小波域重建等效.在此基础上,提出可以较好地修复尖峰噪声的K空间部分重建算法.即在迭代过程中,以图像的稀疏性作为约束条件,仅修改尖峰噪声所遮盖区域的数据,其他位置的数据保持不变.该算法与传统的插值算法及共轭梯度算法相比,能够更好地修复K空间尖峰噪声点,减少图像伪影,同时降低了对尖峰噪声定位准确性的要求.     

Efficient large-array k-domain parallel MRI using channel-by-channel array reduction

This article presents a method to explore the flexibility of channel reduction in k-domain parallel imaging (PI) with massive arrays to improve the computation efficiency. In PI, computation cost increases with the number of channels. For the k-domain methods requiring channel-by-channel reconstruction, this increase can be significant with massive arrays. In this article, a method for efficient k-domain PI reconstruction in large array systems is proposed. The method is based on the fact that in large arrays the channel sensitivity is localized, which allows channel reduction through channel cross correlation. The method is tested with simulated and in vivo MRI data from a 32-channel and 64-channel systems using the multicolumn multiline interpolation (MCMLI) method. Results show that the proposed algorithm can achieve similar or improved reconstruction quality with significantly reduced computation time for massive arrays with localized sensitivity.     

Non-Iterative Regularized reconstruction Algorithm for Non-CartesiAn MRI: NIRVANA

We introduce a novel noniterative algorithm for the fast and accurate reconstruction of nonuniformly sampled MRI data. The proposed scheme derives the reconstructed image as the nonuniform inverse Fourier transform of a compensated dataset. We derive each sample in the compensated dataset as a weighted linear combination of a few measured k-space samples. The specific k-space samples and the weights involved in the linear combination are derived such that the reconstruction error is minimized. The computational complexity of the proposed scheme is comparable to that of gridding. At the same time, it provides significantly improved accuracy and is considerably more robust to noise and undersampling. The advantages of the proposed scheme makes it ideally suited for the fast reconstruction of large multidimensional datasets, which routinely arise in applications such as f-MRI and MR spectroscopy. The comparisons with state-of-the-art algorithms on numerical phantoms and MRI data clearly demonstrate the performance improvement.     

Methods for quantitative image quality evaluation of MRI parallel reconstructions: detection and perceptual difference model

Many reconstruction algorithms are being proposed for parallel magnetic resonance imaging (MRI), which uses multiple coils and subsampled k-space data, and a quantitative method for comparison of algorithms is sorely needed. On such images, we compared three methods for quantitative image quality evaluation: human detection, computer detection model and a computer perceptual difference model (PDM). One-quarter sampling and three different reconstruction methods were investigated: a regularization method developed by Ying et al., a simplified regularization method and an iterative method proposed by Pruessmann et al. Images obtained from a full complement of k-space data were also included as reference images. Detection studies were performed using a simulated dark tumor added on MR images of fresh bovine liver. Human detection depended strongly on reconstruction methods used, with the two regularization methods achieving better performance than the iterative method. Images were also evaluated using detection by a channelized Hotelling observer model and by PDM scores. Both predicted the same trends as observed from human detection. We are encouraged that PDM gives trends similar to that for human detection studies. Its ease of use and applicability to a variety of MRI situations make it attractive for evaluating image quality in a variety of MR studies.