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.     

一种结合并行成像和压缩感知的快速磁共振成像新方法

压缩感知（CS）技术和并行成像技术（主要是SENSE技术、GRAPPA技术等）都能通过减少k空间数据的采集量来加快磁共振成像速度,目前已有一些将两种方法相结合进一步加速磁共振成像速度的方法（例如CS-GRAPPA）.本文针对数据采集和重建这两方面对现有CS-GRAPPA方法进行了改进,采集方式上采用了局部等间隔采集模板以满足GRAPPA重建的要求,并对采集模板进行随机放置以满足CS重建的要求;数据重建时,根据自动校正数据估算GRAPPA算法中欠采行的重建误差,并利用误差的大小确定在CS算法中保真的程度.不同磁共振图像重建实验的结果表明：与现有方法相比,本文方法能够更好地保留原有图像细节并有效减少伪影.     

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.     

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.     

用于压缩感知磁共振成像的分割字典学习算法

字典学习算法可以根据数据本身的特点构建稀疏域中的基,从而使数据的表示更加稀疏.该文在传统的字典学习算法基础上提出了分割字典学习算法,由于部分磁共振图像组织结构简单、可以进行图像分割,因此可根据此特点来优化字典中基函数的构建,使磁共振图像的表达更为稀疏,从而获得更高的重建图像质量.该文利用模拟数据和真实数据进行了重建实验,结果表明与传统的字典学习算法相比,分割字典学习算法能进一步改善重建图像质量.     

基于同时多层激发和并行成像的心脏磁共振电影成像

磁共振成像（MRI）无创无害、对比度多、可以任意剖面成像的特点特别适合用于心脏成像,却因扫描时间长限制了其在临床上的应用.为了解决心脏磁共振电影成像屏气扫描时间过长的问题,该文提出了一种基于同时多层激发的多倍加速心脏磁共振电影成像及其影像重建的方法,该方法将相位调制多层激发（CAIPIRINHA）技术与并行加速（PPA）技术相结合,运用到分段采集心脏电影成像序列中,实现了在相位编码方向和选层方向的四倍加速,并使用改进的SENSE/GRAPPA算法对图像进行重建.分别在水模以及人体上进行了实验,将加速序列图像与不加速序列图像进行对比,结果验证了重建算法的有效性,表明该方法可以在保障图像质量以及准确测量心脏功能的前提下成倍节省扫描时间.     

基于同伦l0范数最小化重建的三维动态磁共振成像

高欠采倍数的动态磁共振图像重建具有重要意义,是同时实现高时间分辨率和高空间分辨率动态对比度增强成像的重要环节.本研究提出一种结合黄金角变密度螺旋采样、并行成像和基于同伦l₀范数最小化的压缩感知的图像重建的三维动态磁共振成像方法.黄金角变密度螺旋采样轨迹被用来连续获取k空间数据,具有数据采集效率高、对运动不敏感等优点.在重建算法中,将多线圈稀疏约束应用于时间总变分域,使用基于l₀范数最小化的非线性重建算法代替传统的l₁范数最小化算法,进一步提高了欠采样率.仿真实验和在体实验表明本文所提的方法在保持图像质量的同时,也可以实现较高的空间分辨率和时间分辨率,初步验证了基于同伦l₀范数最小化重建在三维动态磁共振成像上的优势和临床价值.     

一种数字微镜阵列分区控制和超分辨重建的压缩感知成像法

提出一种压缩感知成像框架结构.该结构采样端用新建的采样矩阵实现数字微镜阵列分区控制,可增强信息获取的准确性,测量得到与新数字微镜阵列对应的压缩采样值;重构端由采样值优化重构出低分辨率图像后,根据分区控制过程建立压缩感知理论框架下的超分辨重建模型,利用梯度稀疏约束优化算法进行求解,恢复出原高分辨率图像.实验结果表明:数字微镜阵列分区控制与超分辨重建相结合的方法可以明显降低压缩感知成像系统的计算量,缩短成像时间,并且具有较高的图像重构质量.     

基于非均匀螺旋线数据和布雷格曼迭代的快速磁共振成像方法

数据采集时间长是制约磁共振成像技术发展的重要瓶颈.为了解决这一问题, 本文基于压缩感知成像理论, 提出了一种结合非均匀螺旋线磁共振数据采集序列和布雷格曼迭代重建的快速磁共振成像方法, 通过欠采样缩短数据采集时间.欠采样引起混迭伪影则通过非均匀螺旋线欠采样特性和布雷格曼迭代重建去除.水模磁共振成像实验和在体磁共振成像实验结果表明: 欠采样情况下, 所提出的方法能有效去除欠采样导致的混迭伪影, 获得的图像结构信息完整的成像结果, 在缩短采样时间的同时, 具有较高的准确度. 关键词： 磁共振成像 非均匀螺旋线 全变分 布雷格曼迭代     

基于lp范数的压缩感知图像重建算法研究

图像重建是光学成像、光声成像、声纳成像、核磁共振成像、 天体成像等物理成像领域中的关键技术之一. 近年来提出的压缩感知理论指出: 对稀疏或者可压缩信号进行少量非自适应线性投影,投影信号含有足够的信息, 从而能对信号进行高概率重建. 压缩感知已被应用于多种物理成像系统. 将罚函数法和修正Hesse阵序列二次规划方法相结合, 并采用了分块压缩感知思想, 提出一种基于l_p范数的压缩感知图像重建算法. 以cameraman, barbara和mandrill图像为例, 采用该算法进行图像重建. 首先, 在不同采样率下对图像重建. 即便采样率低至0.3时, 也能获得高达32.23dB的信噪比, 重建图像清晰可辨. 验证了该算法的正确性. 其次, 将该算法与正交匹配追踪算法进行对比, 在采样率达到0.5以上时, 能够获得高信噪比的重建图像, 成像时间也大为减少, 特别是采样率为0.7时, 成像时间减少88%. 最后, 与现有基于l_p 范数的压缩感知图像重建算法进行对比, 计算结果表明在成像质量有所提高的基础上, 成像时间大为缩短. 关键词： 图像重建 压缩感知 罚函数 修正Hesse阵序列二次规划     

Compressed sensing MR image reconstruction using a motion-compensated reference

Compressed sensing (CS)-based methods have been proposed for image reconstruction from undersampled magnetic resonance data. Recently, CS-based schemes using reference images have also been proposed to further reduce the sampling requirement. In this study, we propose a new reference-constrained CS reconstruction method that accounts for the misalignment between the reference and the target image to be reconstructed. The proposed method uses a new image model that represents the target image as a linear combination of a motion-dependent reference image and a sparse difference image. We then use an efficient iterative algorithm to jointly estimate the motion parameters and the difference image from sparsely sampled data. Simulation results from a numerical phantom data set and an in vivo data set show that the proposed method can accurately compensate the motion effects between the reference and the target images and improve reconstruction quality. The proposed method should prove useful for several applications such as interventional imaging, longitudinal imaging studies and dynamic contrast-enhanced imaging.     

Exploiting the wavelet structure in compressed sensing MRI

Sparsity has been widely utilized in magnetic resonance imaging (MRI) to reduce k-space sampling. According to structured sparsity theories, fewer measurements are required for tree sparse data than the data only with standard sparsity. Intuitively, more accurate image reconstruction can be achieved with the same number of measurements by exploiting the wavelet tree structure in MRI. A novel algorithm is proposed in this article to reconstruct MR images from undersampled k-space data. In contrast to conventional compressed sensing MRI (CS-MRI) that only relies on the sparsity of MR images in wavelet or gradient domain, we exploit the wavelet tree structure to improve CS-MRI. This tree-based CS-MRI problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved by an iterative scheme. Simulations and in vivo experiments demonstrate the significant improvement of the proposed method compared to conventional CS-MRI algorithms, and the feasibleness on MR data compared to existing tree-based imaging algorithms.     

Motion correction based reconstruction method for compressively sampled cardiac MR imaging

Respiratory motion during Magnetic Resonance (MR) acquisition causes strong blurring artifacts in the reconstructed images. These artifacts become more pronounced when used with the fast imaging reconstruction techniques like compressed sensing (CS). Recently, an MR reconstruction technique has been done with the help of compressed sensing (CS), to provide good quality sparse images from the highly under-sampled k-space data. In order to maximize the benefits of CS, it is obvious to use CS with the motion corrected samples. In this paper, we propose a novel CS based motion corrected image reconstruction technique. First, k-space data have been assigned to different respiratory state with the help of frequency domain phase correlation method. Then, multiple sparsity constraints has been used to provide good quality reconstructed cardiac cine images with the highly under-sampled k-space data. The proposed method exploits the multiple sparsity constraints, in combination with demon based registration technique and a novel reconstruction technique to provide the final motion free images. The proposed method is very simple to implement in clinical settings as compared to existing motion corrected methods. The performance of the proposed method is examined using simulated data and clinical data. Results show that this method performs better than the reconstruction of CS based method of cardiac cine images. Different acceleration rates have been used to show the performance of the proposed method.     

Compressed Sensing MRI Using Sparsity Averaging and FISTA

Magnetic resonance imaging (MRI) is widely adopted for clinical diagnosis due to its non-invasively detection. However, acquisition of full k-space data limits its imaging speed. Compressed sensing (CS) provides a new technique to significantly reduce the measurements with high-quality MR image reconstruction. The sparsity of the MR images is one of the crucial bases of CS-MRI. In this paper, we present to use sparsity averaging prior for CS-MRI reconstruction in the basis of that MR images have average sparsity over multiple wavelet frames. The problem is solved using a Fast Iterative Shrinkage Thresholding Algorithm (FISTA), each iteration of which includes a shrinkage step. The performance of the proposed method is evaluated for several types of MR images. The experiment results illustrate that our approach exhibits a better performance than those methods that using redundant frame or a single orthonormal basis to promote sparsity.     

Three dimension double inversion recovery gray matter imaging using compressed sensing

The double inversion recovery (DIR) imaging technique has various applications such as black blood magnetic resonance imaging and gray/white matter imaging. Recent clinical studies show the promise of DIR for high resolution three dimensional (3D) gray matter imaging. One drawback in this case however is the long data acquisition time needed to obtain the fully sampled 3D spatial frequency domain (k-space) data. In this paper, we propose a method to solve this problem using the compressed sensing (CS) algorithm with contourlet transform. The contourlet transform is an effective sparsifying transform especially for images with smooth contours. Therefore, we applied this algorithm to undersampled DIR images and compared with a CS algorithm using wavelet transform by evaluating the reconstruction performance of each algorithm for undersampled k-space data. The results show that the proposed CS algorithm achieves a more accurate reconstruction in terms of the mean structural similarity index and root mean square error than the CS algorithm using wavelet transform.     

Joint reconstruction of multiecho MR images using correlated sparsity

This works addresses the problem of reconstructing multiple T1- or T2-weighted images of the same anatomical cross section from partially sampled K-space data. Previous studies in reconstructing magnetic resonance (MR) images from partial samples of the K-space used compressed sensing (CS) techniques to exploit the spatial correlation of the images (leading to sparsity in wavelet domain). Such techniques can be employed to reconstruct the individual T1- or T2-weighted images. However, in the current context, the different images are not really independent; they are images of the same cross section and, hence, are highly correlated. We exploit the correlation between the images, along with the spatial correlation within the images to achieve better reconstruction results than exploiting spatial correlation only.For individual MR images, CS-based techniques lead to a sparsity-promoting optimization problem in the wavelet domain. In this article, we show that the same framework can be extended to incorporate correlation between images leading to group/row sparsity-promoting optimization. Algorithms for solving such optimization problems have already been developed in the CS literature. We show that significant improvement in reconstruction accuracy can be achieved by considering the correlation between different T1- and T2-weighted images. If the reconstruction accuracy is considered to be constant, our proposed group sparse formulation can yield the same result with 33% less K-space samples compared with simple sparsity-promoting reconstruction. Moreover, the reconstruction time by our proposed method is about two to four times less than the previous method.