More IMPATIENT: A gridding-accelerated Toeplitz-based strategy for non-Cartesian high-resolution 3D MRI on GPUs

Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code.     

Low Rank Prior and Total Variation Regularization for Image Deblurring

The similar image patches should have similar underlying structures. Thus the matrix constructed from stacking the similar patches together has low rank. Based on this fact, the nuclear norm minimization, which is the convex relaxation of low rank minimization, leads to good denoising results. Recently, the weighted nuclear norm minimization has been applied to image denoising. This approach presents state-of-the-art result for image denoising. In this paper, we further study the weighted nuclear norm minimization problem for general image recovery task. For the weights being in arbitrary order, we prove that such minimization problem has a unique global optimal solution in the closed form. Incorporating this idea with the celebrated total variation regularization, we then investigate the image deblurring problem. Numerical experimental results illustratively clearly that the proposed algorithms achieve competitive performance.     

基于变量分裂法的稀疏约束并行磁共振图像重建

针对并行磁共振成像技术中,数据欠采样造成重建图像存在的混迭伪影和噪声问题,提出一种稀疏约束下并行磁共振的图像重建算法。该算法将一阶差分作为稀疏投影算子,构建在各向异性全变分最小化约束下并行磁共振的图像重建问题。同时,提出基于变量分裂法的求解方法,并在不同实验环境下分析该算法的有效性和鲁棒性。结果表明该算法可显著提高加速因子最大时并行磁共振重建图像的质量。     

A distributed computing system for magnetic resonance imaging: Java-based processing and binding of XML

Recently we have developed a Java-based heterogeneous distributed computing system for the field of magnetic resonance imaging (MRI). It is a software system for embedding the various image reconstruction algorithms that we have created for handling MRI data sets with sparse sampling distributions. Since these data sets may result from multi-dimensional MRI measurements our system has to control the storage and manipulation of large amounts of data. In this paper we describe how we have employed the extensible markup language (XML) to realize this data handling in a highly structured way. To that end we have used Java packages, recently released by Sun Microsystems, to process XML documents and to compile pieces of XML code into Java classes. We have effectuated a flexible storage and manipulation approach for all kinds of data within the MRI system, such as data describing and containing multi-dimensional MRI measurements, data configuring image reconstruction methods and data representing and visualizing the various services of the system. We have found that the object-oriented approach, possible with the Java programming environment, combined with the XML technology is a convenient way of describing and handling various data streams in heterogeneous distributed computing systems.     

Reweighted minimization model for MR image reconstruction with split Bregman method

Magnetic resonance(MR) image reconstruction is to get a practicable gray-scale image from few frequency domain coefficients.In this paper,different reweighted minimization models for MR image reconstruction are studied,and a novel model named reweighted wavelet+TV minimization model is proposed.By using split Bregman method,an iteration minimization algorithm for solving this new model is obtained,and its convergence is established.Numerical simulations show that the proposed model and its algorithm are feasible and highly efficient.     

基于场量提取法的电磁层析成像系统的灵敏度推算

电磁层析成像技术(EMT)是一种新型的电学层析成像技术,它通过测量激励和接受线圈之间的互感变化而实现物场区域内电导率和磁导率分布的图像重建.灵敏度的计算是电磁层析成像技术的关键环节,是图像重建的必备条件,灵敏度计算的准确性直接影响到最终的成像精度.采用场量提取的方法计算了EMT系统的灵敏度.理论上,首次完整地推导出了E...     

深度学习的快速磁共振成像及欠采样轨迹设计

目的 快速成像一直是磁共振成像（MRI）技术中的焦点之一,现有多通道并行成像和部分k空间数据重建都是通过减少梯度编码步数来降低数据的获取时间,两者结合起来更能有效地提高扫描速度。然而,在欠采样倍数加高的情况下,依然有很严重的混叠伪影,因此研究一种在保证成像精度的前提下加快成像速度的方法尤为重要。方法 基于卷积神经网络的磁共振成像（CNN-MRI）方法利用大量现有的全采样多通道数据的先验信息,设计并线下训练一个深度卷积神经网络,学习待重建图像与全采样图像之间的映射关系,从而在线上成像时,欠采样所丢失数据能被训练好的网络进行预测。本文探讨了对于深度学习磁共振成像的可选择性欠采样方式,提出了一种新的欠采样轨迹方案。为了判断本文方法的性能,用峰值信噪比（PSNR）、结构相似度（SSIM）以及均方根差（RMSE）来作为衡量的指标。结果 实验结果表明,所提出欠采样方案的综合性能要优于传统欠采样轨迹,PSNR要高出12 dB,SSIM高出近0.1,RMSE要降低0.020.04左右。此外重建结果还与经典的并行重建方法GRAPPA（geneRalized autocalibrating partially parallel acquisitions）、SPIRiT（iterative self-consistent parallel imaging reconstruction from arbitrary k-space）以及SAKE（simultaneous autocalibrating and k-space estimation）作比较,从视觉效果以及各项量化指标得出本文方法能重建出更准确的结果,并且重建速度要快5倍以上。结论 深度学习方法能很好地在线下训练时从大量数据集中提取并学习到有价值的先验信息,所以在线上测试时能在较短时间内重建出优于经典算法的高质量结果;提出的1维低频汉明滤波欠采样方案则有利于提升该网络的性能。     

Subsampled terahertz data reconstruction based on spatio-temporal dictionary learning

In this paper, the problem of terahertz pulsed imaging and reconstruction is addressed. It is assumed that an incomplete (subsampled) three dimensional THz data set has been acquired and the aim is to recover all missing samples. A sparsity-inducing approach is proposed for this purpose. First, a simple interpolation is applied to incomplete noisy data. Then, we propose a spatio-temporal dictionary learning method to obtain an appropriate sparse representation of data based on a joint sparse recovery algorithm. Then, using the sparse coefficients and the learned dictionary, the 3D data is effectively denoised by minimizing a simple cost function. We consider two types of terahertz data to evaluate the performance of the proposed approach: THz data acquired for a model sample with clear layered structures (e.g., a T-shape plastic sheet buried in a polythene pellet), and pharmaceutical tablet data (with low spatial resolution). The achieved signal-to-noise-ratio for reconstruction of T-shape data, from only 5% observation was 19 dB. Moreover, the accuracies of obtained thickness and depth measurements for pharmaceutical tablet data after reconstruction from 10% observation were 98.8%, and 99.9%, respectively. These results, along with chemical mapping analysis, presented at the end of this paper, confirm the accuracy of the proposed method.     

基于多通道并行采集的部分可分离函数高分辨动态磁共振成像

部分可分离函数(Partial Separability,PS)是一种高分辨动态磁共振稀疏成像模型,可以对心脏等运动目标实现高 分辨动态成像,然而该模型需要充足的扫描数据才能进行图像重建,因此存在扫描时间较长的缺点。文章在 PS 模型基础 上,利用并行成像原理对磁共振数据进行降采样,从而缩短 PS 模型的扫描时间。数学仿真和载体实验结果表明,该方法 可以准确重建出高时空分辨率磁共振图像并且将扫描速度提高 2～3 倍。     

从压缩传感到低秩矩阵恢复: 理论与应用

综述了压缩传感、矩阵秩最小化和低秩矩阵恢复等方面的基础理论及典型应用. 基于凸优化的压缩传感及由其衍生的矩阵秩最小化和低秩矩阵恢复是近年来的研究热点,在信号处理、 推荐系统、高维数据分析、图像处理、计算机视觉等很多研究领域具有重要和成功的应用. 在这些实际的应用中,往往涉及到对高维数据的分析与处理,需要充分和合理利用数据中的如稀疏性或其所构成矩阵的低秩性等性质. 尽管在最坏情况下,最小化诸如稀疏性或矩阵秩这样的目标函数是 NP 难的,但是在某些合理的假设条件下,通过优化目标函数的凸松弛替代函数, 采用凸优化的方法,能够精确地给出原问题的最优解. 有很多高效的凸优化算法对之进行求解且适用于大规模问题.本文首先分别综述了压缩传感、 矩阵秩最小化和低秩矩阵恢复的相关基础理论,然后对其在图像处理、计算机视觉和计算摄像学等领域的典型应用予以举例介绍,并展望了相关领域未来的研究工作.     

SAR image reconstruction and autofocus by compressed sensing

A new SAR signal processing technique based on compressed sensing is proposed for autofocused image reconstruction on subsampled raw SAR data. It is shown that, if the residual phase error after INS/GPS corrected platform motion is captured in the signal model, then the optimal autofocused image formation can be formulated as a sparse reconstruction problem. To further improve image quality, the total variation of the reconstruction is used as a penalty term. In order to demonstrate the performance of the proposed technique in wide-band SAR systems, the measurements used in the reconstruction are formed by a new under-sampling pattern that can be easily implemented in practice by using slower rate A/D converters. Under a variety of metrics for the reconstruction quality, it is demonstrated that, even at high under-sampling ratios, the proposed technique provides reconstruction quality comparable to that obtained by the classical techniques which require full-band data without any under-sampling.     

基于自适应稀疏表达的并行磁共振重建方法

为精确地进行并行磁共振成像,文章利用字典学习的强大捕捉细节和稀疏开发能力,提出了一种基于自适应稀疏表达的重建方法。该方法将并行磁共振重建问题转化为最小化由字典学习和数据拟合项构成的目标函数,并采用了分而治之的方案求解未知变量。为验证其有效性,将该方法与目前主流的两种方法在人体实际磁共振数据上进行了测试。测试结果显示,文章提出的方法能在抑制图像噪声的同时较好地保存图像细节。     

加权低秩矩阵恢复的混合噪声图像去噪

传统的基于低秩矩阵恢复的图像去噪算法只对低秩部分进行约束,当高斯噪声过大时,会导致去噪不充分或细节严重丢失。针对此问题,提出了一种新的鲁棒的图像去噪模型。该模型在原有的低秩矩阵核范数约束的基础上引入高斯噪声约束项,此外为了提高低秩矩阵的低秩性和稀疏矩阵的稀疏性,引入了加权的方法。为了考察方法的去噪能力,选取了不同参数类型的混合噪声图像进行仿真,并结合峰值信噪比、结构相似度评价标准与传统的基于低秩矩阵恢复的图像去噪算法进行对比。实验结果表明,加权低秩矩阵恢复的混合噪声图像去噪算法能增加低秩矩阵的低秩性和稀疏矩阵的稀疏性,在保证去噪效果的同时,保留了图像的细节信息,具有更佳的视觉效果,同时,客观评价指标均有所提高。     

Camera calibration based on arbitrary parallelograms

Existing algorithms for camera calibration and metric reconstruction are not appropriate for image sets containing geometrically transformed images for which we cannot apply the camera constraints such as square or zero-skewed pixels. In this paper, we propose a framework to use scene constraints in the form of camera constraints. Our approach is based on image warping using images of parallelograms. We show that the warped image using parallelograms constrains the camera both intrinsically and extrinsically. Image warping converts the calibration problems of transformed images into the calibration problem with highly constrained cameras. In addition, it is possible to determine affine projection matrices from the images without explicit projective reconstruction. We introduce camera motion constraints of the warped image and a new parameterization of an infinite homography using the warping matrix. Combining the calibration and the affine reconstruction results in the fully metric reconstruction of scenes with geometrically transformed images. The feasibility of the proposed algorithm is tested with synthetic and real data. Finally, examples of metric reconstructions are shown from the geometrically transformed images obtained from the Internet.     

Robust alternative minimization for matrix completion

Recently, much attention has been drawn to the problem of matrix completion, which arises in a number of fields, including computer vision, pattern recognition, sensor network, and recommendation systems. This paper proposes a novel algorithm, named robust alternative minimization (RAM), which is based on the constraint of low rank to complete an unknown matrix. The proposed RAM algorithm can effectively reduce the relative reconstruction error of the recovered matrix. It is numerically easier to minimize the objective function and more stable for large-scale matrix completion compared with other existing methods. It is robust and efficient for low-rank matrix completion, and the convergence of the RAM algorithm is also established. Numerical results showed that both the recovery accuracy and running time of the RAM algorithm are competitive with other reported methods. Moreover, the applications of the RAM algorithm to low-rank image recovery demonstrated that it achieves satisfactory performance.     

Constrained Projection Approximation Algorithms for Principal Component Analysis

In this paper, we introduce a new error measure, integrated reconstruction error (IRE) and show that the minimization of IRE leads to principal eigenvectors (without rotational ambiguity) of the data covariance matrix. Then, we present iterative algorithms for the IRE minimization, where we use the projection approximation. The proposed algorithm is referred to as COnstrained Projection Approximation (COPA) algorithm and its limiting case is called COPAL. Numerical experiments demonstrate that these algorithms successfully find exact principal eigenvectors of the data covariance matrix.     

Consistent Shape Maps via Semidefinite Programming

Recent advances in shape matching have shown that jointly optimizing the maps among the shapes in a collection can lead to significant improvements when compared to estimating maps between pairs of shapes in isolation. These methods typically invoke a cycle‐consistency criterion — the fact that compositions of maps along a cycle of shapes should approximate the identity map. This condition regularizes the network and allows for the correction of errors and imperfections in individual maps. In particular, it encourages the estimation of maps between dissimilar shapes by compositions of maps along a path of more similar shapes. In this paper, we introduce a novel approach for obtaining consistent shape maps in a collection that formulates the cycle‐consistency constraint as the solution to a semidefinite program (SDP). The proposed approach is based on the observation that, if the ground truth maps between the shapes are cycle‐consistent, then the matrix that stores all pair‐wise maps in blocks is low‐rank and positive semidefinite. Motivated by recent advances in techniques for low‐rank matrix recovery via semidefinite programming, we formulate the problem of estimating cycle‐consistent maps as finding the closest positive semidefinite matrix to an input matrix that stores all the initial maps. By analyzing the Karush‐Kuhn‐Tucker (KKT) optimality condition of this program, we derive theoretical guarantees for the proposed algorithm, ensuring the correctness of the recovery when the errors in the inputs maps do not exceed certain thresholds. Besides this theoretical guarantee, experimental results on benchmark datasets show that the proposed approach outperforms state‐of‐the‐art multiple shape matching methods.     

State Estimation with Structural Priors in fMRI

We propose a state estimation approach for functional magnetic resonance imaging (fMRI). In state estimation, time-dependent image reconstruction problem is modeled by separate state evolution and observation models, and the objective is to estimate the time series of system states, given the models and the time-dependent measurement data. Our method computes the state estimates by using the Kalman filter (KF) and Kalman smoother (KS) algorithms. We propose to complement the state estimation formulation with a structural prior which can be derived from the anatomical MRI, acquired as a part of the fMRI protocol. Two different constructions of the structural prior are considered. The first one is a structured smoothness prior where the state observation matrix is augmented with a spatially weighted regularization matrix which promotes structural similarity of the gradient of the unknown image with the gradient of the anatomical image. The second approach is based on applying structured total variation denoising to the KF estimate at each time step of the Kalman recursions. The proposed approaches are evaluated using simulated and experimental, radially sampled, small animal fMRI data from a rat brain. In our method, the state estimates are updated after each new spoke of radial data becomes available, leading to faster frame rate compared to the conventional image reconstruction approaches. The results are compared to a sliding window method and a conventional reconstruction which produces new image only after a full circle of k-space spokes becomes available. The results suggest that the state estimation approach with the structural prior can improve both spatial and temporal resolution of fMRI.     

Variable reconstruction and sensor fault identification using canonical variate analysis

The detection and identification of faults in dynamic continuous processes has received considerable recent attention from researchers in academia and industry. In this paper, a canonical variate analysis (CVA)-based sensor fault detection and identification method via variable reconstruction is described. Several previous studies have shown that CVA-based monitoring techniques can effectively detect faults in dynamic processes. Here we define two monitoring indices in the state and noise spaces for fault detection and, for sensor fault identification, we propose three variable reconstruction algorithms based on the proposed monitoring indices. The variable reconstruction algorithms are based on the concepts of conditional mean replacement and object function minimization. The proposed approach is applied to a simulated continuous stirred tank reactor and the results are compared to those obtained using the traditional dynamic monitoring technique, dynamic principal component analysis (PCA). The results indicate that the proposed methodology is quite effective for monitoring dynamic processes in terms of sensor fault detection and identification.     

Compressive Volume Rendering

Compressive rendering refers to the process of reconstructing a full image from a small subset of the rendered pixels, thereby expediting the rendering task. In this paper, we empirically investigate three image order techniques for compressive rendering that are suitable for direct volume rendering. The first technique is based on the theory of compressed sensing and leverages the sparsity of the image gradient in the Fourier domain. The latter techniques exploit smoothness properties of the rendered image; the second technique recovers the missing pixels via a total variation minimization procedure while the third technique incorporates a smoothness prior in a variational reconstruction framework employing interpolating cubic B‐splines. We compare and contrast the three techniques in terms of quality, efficiency and sensitivity to the distribution of pixels. Our results show that smoothness‐based techniques significantly outperform techniques that are based on compressed sensing and are also robust in the presence of highly incomplete information. We achieve high quality recovery with as little as 20% of the pixels distributed uniformly in screen space.