PEAR：周期性和固定秩分离，用于快速fMRI
PEAR: PEriodic And fixed Rank separation for fast fMRI
摘要：
在功能磁共振成像（fMRI）中，通过欠采样数据的更快的采集可以改善时空分辨率的权衡，并通过增加自由度来增加统计鲁棒性。从欠采样测量中重建高质量的fMRI数据需要对数据进行适当的建模。我们提出了一种fMRI重建方法的基础上建模的fMRI信号作为一个周期性和固定的秩分量的总和，改善重建欠采样测量。我们将fMRI信号分解成一个具有固定秩的分量和一个由在时间傅立叶域中稀疏的周期信号之和组成的分量。数据重建是通过解决一个约束问题，强制执行一个固定的，适度的排名的组件之一，和有限数量的时间频率的其他。我们的方法被称为PEAR - PEriodic And fixed Rank separation for fast fMRI。实验结果包括纯粹的合成模拟、实时时间过程的模拟以及对真实fMRI数据集的回顾性欠采样。评估进行定量和视觉与地面实况，比较PEAR的两个额外的最近的方法，从欠采样测量的功能磁共振成像重建。结果表明，PEAR的改进估计的时间过程和激活地图的方法相比，在加速比R= 8，16（模拟数据）和R= 6.66，10（真实数据）。与使用基于固定秩的模型或传统的低秩+稀疏算法相比，PEAR的重建具有更高的保真度。我们已经表明，分裂组件之间的功能信息，导致更好的fMRI建模，超过国家的最先进的方法。
英文摘要：
In functional MRI (fMRI), faster acquisition via undersampling of data can improve the spatial-temporal resolution trade-off and increase statistical robustness through increased degrees-of-freedom. High quality reconstruction of fMRI data from undersampled measurements requires proper modeling of the data. We present an fMRI reconstruction approach based on modeling the fMRI signal as a sum of periodic and fixed rank components, for improved reconstruction from undersampled measurements. We decompose the fMRI signal into a component which a has fixed rank and a component consisting of a sum of periodic signals which is sparse in the temporal Fourier domain. Data reconstruction is performed by solving a constrained problem that enforces a fixed, moderate rank on one of the components, and a limited number of temporal frequencies on the other. Our approach is coined PEAR - PEriodic And fixed Rank separation for fast fMRI. Experimental results include purely synthetic simulation, a simulation with real timecourses and retrospective undersampling of a real fMRI dataset. Evaluation was performed both quantitatively and visually versus ground truth, comparing PEAR to two additional recent methods for fMRI reconstruction from undersampled measurements. Results demonstrate PEAR's improvement in estimating the timecourses and activation maps versus the methods compared against at acceleration ratios of R=8,16 (for simulated data) and R=6.66,10 (for real data). PEAR results in reconstruction with higher fidelity than when using a fixed-rank based model or a conventional Low-rank+Sparse algorithm. We have shown that splitting the functional information between the components leads to better modeling of fMRI, over state-of-the-art methods.
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