Robust principle component analysis based four-dimensional computed tomography-猫眼课题宝

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2010

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Hao Gao;Jian-Feng Cai;Zuowei Shen;Hongkai Zhao

.这篇文章的目的是四维（4D）计算机断层扫描（CT）是三重。(1)从矩阵的角度提出了一种新的时空模型，即基于4DCT的Robust PCA模型（Robust Principle Component Analysis based 4DCT）。也就是说，而不是查看的三维（3D）图像的时间集合的4D对象，并寻找在时间或空间上的局部相干性独立，我们认为它作为一个低秩矩阵和稀疏矩阵的混合物，以探索相位之间的空间结构的最大时间相干性。这里，低秩矩阵对应于“背景”或参考状态，其随时间静止或在结构上类似;稀疏矩阵代表“运动”或时变分量，例如，心脏成像中的心脏运动，其本身通常是近似稀疏的，或者可以在适当的基础上被稀疏化。除了4D CT之外，这种基于鲁棒PCA的4DCT模型还可以应用于其他成像问题，例如多能量CT，心脏MRI和高光谱成像，以最少的数据量进行运动减少或/和变化检测。(2)数据采集的动态策略，即，提出了一种时间螺旋方案，其可以潜在地用少得多的数据投影来保持类似的重建精度。这种动态方案的关键点是通过在不同阶段获取互补数据，同时减少对共同背景结构的冗余测量，从而减少测量的总数，从而减少辐射剂量。(3)本文提出了一种基于分裂Bregman方法的精确、高效、易于实现的算法，用于求解紧框架下的稀疏表示模型问题

. The purpose of this article for four-dimensional (4D) computed tomography (CT) is three-fold. (1) A new spatiotemporal model is presented from matrix perspective with the row dimension in space and the column dimension in time, namely, Robust PCA based 4DCT model (Robust Principle Component Analysis based 4D CT). That is, instead of viewing the 4D object as a temporal collection of three-dimensional (3D) images and looking for local coherence in time or space independently, we perceive it as a mixture of low-rank matrix and sparse matrix to explore the maximum temporal coherence of spatial structure among phases. Here the low-rank matrix corresponds to the “background” or reference state, which is stationary over time or similar in structure; the sparse matrix stands for the “motion” or time-varying component, e.g., heart motion in cardiac imaging, which is often either approximately sparse itself or can be sparsified in the proper basis. Besides 4D CT, this Robust PCA based 4DCT model should be applicable in other imaging problems for motion reduction or/and change detection with the least amount of data, such as multi-energy CT, cardiac MRI, and hyperspectral imaging. (2) A dynamic strategy for data acquisition, i.e., a temporally spiral scheme, is proposed that can potentially maintain the similar reconstruction accuracy with much fewer projections of the data. The key point of this dynamic scheme is to reduce the total number of measurements and hence the radiation dose, by acquiring complementary data in different phases while reducing redundant measurements of the common background structure. (3) An accurate, efficient, yet simple-to-implement algorithm based on split Bregman method is developed for solving the model problem with the sparse representation in tight frames

Robust principle component analysis based four-dimensional computed tomography

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