Volume 30, Issue 5

Compressed sensing (CS) utilizes the sparsity of magnetic resonance (MR) images to enable accurate reconstruction from undersampled k-space data. Recent CS methods have employed analytical sparsifying transforms such as wavelets, curvelets, and finite differences. In this paper, we propose a novel framework for adaptively learning the sparsifying transform (dictionary), and reconstructing the image simultaneously from highly undersampled k-space data. The sparsity in this framework is enforced on overlapping image patches emphasizing local structure. Moreover, the dictionary is adapted to the particular image instance thereby favoring better sparsities and consequently much higher undersampling rates. The proposed alternating reconstruction algorithm learns the sparsifying dictionary, and uses it to remove aliasing and noise in one step, and subsequently restores and fills-in the k-space data in the other step. Numerical experiments are conducted on MR images and on real MR data of several anatomies with a variety of sampling schemes. The results demonstrate dramatic improvements on the order of 4-18 dB in reconstruction error and doubling of the acceptable undersampling factor using the proposed adaptive dictionary as compared to previous CS methods. These improvements persist over a wide range of practical data signal-to-noise ratios, without any parameter tuning.

压缩感知(CS)利用磁共振(MR)图像的稀疏性，从欠采样的k空间数据中实现精确重建。最近的CS方法采用了分析性稀疏变换，如小波、曲线波和有限差分。在本文中，我们提出了一种新颖的框架，用于自适应学习稀疏变换（字典），并同时从重度欠采样的k空间数据中重建图像。该框架中的稀疏性施加在重叠的图像块上，强调局部结构。此外，字典适应于特定的图像实例，从而有利于更好的稀疏性，进而实现更高的欠采样率。所提出的交替重建算法学习稀疏字典，并在一步中使用它去除混叠和噪声，然后在另一步中恢复并填充k空间数据。在MR图像和多种解剖结构的真实MR数据上进行了数值实验，采用了多种采样方案。结果表明，与之前的CS方法相比，使用所提出的自适应字典，重建误差显著提高了4-18 dB，可接受的欠采样因子翻倍。这些改进在广泛的实际数据信噪比范围内持续存在，无需任何参数调整。

We introduce a novel algorithm to reconstruct dynamic magnetic resonance imaging (MRI) data from under-sampled k-t space data. In contrast to classical model based cine MRI schemes that rely on the sparsity or banded structure in Fourier space, we use the compact representation of the data in the Karhunen Louve transform (KLT) domain to exploit the correlations in the dataset. The use of the data-...

我们提出了一种新颖的算法，用于从欠采样的k-t空间数据重建动态磁共振成像（MRI）数据。与依赖于傅里叶空间中稀疏性或带状结构的经典基于模型的电影MRI方案不同，我们利用数据在Karhunen-Loève变换（KLT）域中的紧凑表示来挖掘数据集中的相关性。使用数据-...

We propose a novel statistical analysis method for functional magnetic resonance imaging (fMRI) to overcome the drawbacks of conventional data-driven methods such as the independent component analysis (ICA). Although ICA has been broadly applied to fMRI due to its capacity to separate spatially or temporally independent components, the assumption of independence has been challenged by recent studi...

我们提出了一种新的功能磁共振成像（fMRI）统计分析方法，以克服传统数据驱动方法（如独立成分分析（ICA））的缺点。尽管ICA由于能够分离空间或时间独立成分而被广泛应用于fMRI，但独立性的假设已受到近期研究的挑战……

Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding effects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the small-n large-p situation, a sparseness constraint is generally introduced. In this paper, we consider the sparse linear regression model with a l1-norm penal...

偏相关系数是脑网络中有用的连接性度量，特别是在需要消除高度相关网络中的混杂效应时。由于在小样本大p情况下难以估计精确的偏相关，通常引入稀疏约束。本文考虑带有l1范数惩罚的稀疏线性回归模型...

Despite the relative recency of its inception, the theory of compressive sampling (aka compressed sensing) (CS) has already revolutionized multiple areas of applied sciences, a particularly important instance of which is medical imaging. Specifically, the theory has provided a different perspective on the important problem of optimal sampling in magnetic resonance imaging (MRI), with an ever-incre...

尽管压缩采样（又称压缩感知）理论问世时间相对较短，但它已经彻底改变了应用科学的多个领域，其中尤以医学成像为例。具体来说，该理论为磁共振成像中的最优采样这一重要问题提供了新的视角，且其影响与日俱增...

Diffuse optical tomography (DOT) is a sensitive and relatively low cost imaging modality that reconstructs optical properties of a highly scattering medium. However, due to the diffusive nature of light propagation, the problem is severely ill-conditioned and highly nonlinear. Even though nonlinear iterative methods have been commonly used, they are computationally expensive especially for three d...

扩散光学断层成像（DOT）是一种灵敏且相对低成本的成像模式，可重建高散射介质的光学特性。然而，由于光传播的扩散性质，该问题严重病态且高度非线性。尽管非线性迭代方法已被广泛使用，但计算成本高昂，特别是在三维...

This paper presents a statistical interior tomography (SIT) approach making use of compressed sensing (CS) theory. With the projection data modeled by the Poisson distribution, an objective function with a total variation (TV) regularization term is formulated in the maximization of a posteriori (MAP) framework to solve the interior problem. An alternating minimization method is used to optimize t...

本文提出了一种利用压缩感知理论的统计内部断层成像方法。将投影数据建模为泊松分布，在最大后验估计框架下，构造了带有全变分正则项的目标函数来解决内部重建问题。采用交替最小化方法进行优化...

The problem of high-resolution image volume reconstruction from reduced frequency acquisition sequences has drawn significant attention from the scientific community because of its practical importance in medical diagnosis. To address this issue, several reconstruction strategies have been recently proposed, which aim to recover the missing information either by exploiting the spatio-temporal corr...

从减少频率采集序列中重建高分辨率图像体积的问题因其在医学诊断中的实际重要性而引起了科学界的极大关注。为了解决这个问题，最近提出了几种重建策略，旨在通过利用时空相关性来恢复缺失信息...

In this paper, we present a fast numerical algorithm for solving total variation and $\ell_1$ (TVL1) based image reconstruction with application in partially parallel magnetic resonance imaging. Our algorithm uses variable splitting method to reduce computational cost. Moreover, the Barzilai–Borwein step size selection method is adopted in our algorithm for much faster convergence. Experimental results on clinical partially parallel imaging data demonstrate that the proposed algorithm requires much fewer iterations and/or less computational cost than recently developed operator splitting and Bregman operator splitting methods, which can deal with a general sensing matrix in reconstruction framework, to get similar or even better quality of reconstructed images.

在本文中，我们提出了一种快速数值算法，用于求解基于全变差和ℓ1（TVL1）的图像重建问题，并将其应用于部分并行磁共振成像。我们的算法采用变量分裂方法来降低计算成本。此外，我们在算法中采用了Barzilai-Borwein步长选择方法以实现更快的收敛速度。实验结果...

Coronary magnetic resonance imaging (MRI) is a noninvasive imaging modality for diagnosis of coronary artery disease. One of the limitations of coronary MRI is its long acquisition time due to the need of imaging with high spatial resolution and constraints on respiratory and cardiac motions. Compressed sensing (CS) has been recently utilized to accelerate image acquisition in MRI. In this paper, ...

冠状动脉磁共振成像（MRI）是一种用于诊断冠状动脉疾病的无创成像方式。冠状动脉MRI的局限性之一是其采集时间长，因为需要高空间分辨率成像并受呼吸和心脏运动的限制。最近，压缩感知（CS）被用于加速MRI的图像采集。本文...

In this paper we propose a method based on (2, 1)-mixed-norm penalization for incorporating a structural prior in FDOT image reconstruction. The effect of (2, 1)-mixed-norm penalization is twofold: first, a sparsifying effect which isolates few anatomical regions where the fluorescent probe has accumulated, and second, a regularization effect inside the selected anatomical regions. After formulati...

本文提出了一种基于（2,1）-混合范数惩罚的方法，用于在FDOT图像重建中融入结构先验。（2,1）-混合范数惩罚的效果有两方面：首先，稀疏化效果分离出荧光探针积累的少数解剖区域；其次，在选定的解剖区域内产生正则化效果。

Magnetization-prepared acquisitions offer a trade-off between image contrast and scan efficiency for magnetic resonance imaging. Because the prepared signals gradually decay, the contrast can be improved by frequently repeating the preparation, which in turn significantly increases the scan time. A common solution is to perform the data collection progressing from low- to high-spatial-frequency sa...

磁化准备采集在磁共振成像中提供了图像对比度和扫描效率之间的权衡。由于准备信号逐渐衰减，通过频繁重复准备可以改善对比度，但这会显著增加扫描时间。一种常见的解决方案是从低空间频率到高空间频率进行数据采集...

Compressive sensing (CS) has seen impressive successes and fast growth over the past ten years, including applications in medical imaging. Applications of CS to magnetic resonance imaging (MRI) have been the earliest, most numerous, and most diverse, owing to the tremendous flexibility in designing the acquisition process and the pressing need that MRI has, as a slow acquisition modality, to reduc...

压缩感知在过去十年中取得了令人瞩目的成功和快速发展，包括在医学成像中的应用。压缩感知在磁共振成像中的应用最早、最多样化，这是由于设计采集过程的巨大灵活性以及MRI作为一种缓慢采集模态迫切需要减少...

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