Robust principal component analysis-based four-dimensional computed tomography.
Robust principal component analysis-based four-dimensional computed tomography.
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DOI：
10.1088/0031-9155/56/11/002
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发表时间：
2011-06-07
影响因子：
3.5
通讯作者：
Zhao H
中科院分区：
文献类型：
--
作者：
Gao H;Cai JF;Shen Z;Zhao H
本文针对四维 (4D) 计算机断层扫描 (CT) 的目的有三个。 (1)从矩阵的角度提出了一种空间上为行维、时间上为列维的新时空模型，即基于稳健PCA（主成分分析）的4D CT模型。也就是说，我们不是将 4D 对象视为三维 (3D) 图像的时间集合并独立地寻找时间或空间上的局部相干性，而是将其视为低秩矩阵和稀疏矩阵的混合，以探索各相之间空间结构的最大时间相干性。这里的低秩矩阵对应于“背景”或参考状态，它随着时间的推移是静止的或结构类似；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稀疏化。除了 4D CT 之外，这种基于 PCA 的稳健 4D CT 模型还应该适用于其他成像问题，以最少的数据量进行运动减少或/和变化检测，例如多能量 CT、心脏 MRI 和高光谱成像。 （2）提出了一种数据采集的动态策略，即时间螺旋方案，它可以用更少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获取不同阶段的互补数据同时减少共同背景结构的冗余测量来减少测量总数，从而减少辐射剂量。 (3) 开发了一种基于分裂Bregman方法的准确、高效且易于实现的算法，用于解决紧框架中稀疏表示的模型问题。
The purpose of this paper for four-dimensional (4D) computed tomography (CT) is threefold. (1) A new spatiotemporal model is presented from the matrix perspective with the row dimension in space and the column dimension in time, namely the robust PCA (principal component analysis)-based 4D CT model. 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 the 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 4D CT 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 similar reconstruction accuracy with far 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 the split Bregman method is developed for solving the model problem with sparse representation in tight frames.
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