基于低秩矩阵分解的电影锥束CT重建算法及原理验证
Cine cone beam CT reconstruction using low-rank matrix factorization: algorithm and a proof-of-princple study
摘要：
呼吸相关CBCT，通常称为4DCBCT，提供呼吸相位分辨CBCT图像。在许多临床应用中，更优选的是重建第四维为时间的真实4DCBCT，即，基于相应的瞬时投影来重建每个CBCT图像。在这项工作中，我们提出了一种新的算法重建这种真正的时间分辨CBCT，称为电影CBCT，有效地利用潜在的时间相干性，如周期性或重复，在这些电影CBCT图像。假设矩阵$\bm{U}$的每一列表示要重建的CBCT图像，并且列的总数与投影的数量相同，我们算法的中心思想是$\bm{U}$的秩远小于投影的数量，并且我们可以对$\bm{U}$使用矩阵分解形式$\bm{U}=\bm{L}\bm{R}$。矩阵$\bm{L}$的列数约束$\bm{U}$的秩，因此在电影CBCT中的所有图像之间隐含地施加时间相干性条件。通过分别惩罚$\bm{L}$的紧小波框架变换的稀疏性和$\bm{R}$的傅立叶变换的稀疏性来实现$\bm{L}$中的期望图像属性和呼吸模式的周期性。采用分裂Bregman方法求解该问题。在本文中，我们专注于提出这种新的算法，并显示使用NCAT幻影仿真研究的原理证明。
英文摘要：
Respiration-correlated CBCT, commonly called 4DCBCT, provide respiratory phase-resolved CBCT images. In many clinical applications, it is more preferable to reconstruct true 4DCBCT with the 4th dimension being time, i.e., each CBCT image is reconstructed based on the corresponding instantaneous projection. We propose in this work a novel algorithm for the reconstruction of this truly time-resolved CBCT, called cine-CBCT, by effectively utilizing the underlying temporal coherence, such as periodicity or repetition, in those cine-CBCT images. Assuming each column of the matrix $\bm{U}$ represents a CBCT image to be reconstructed and the total number of columns is the same as the number of projections, the central idea of our algorithm is that the rank of $\bm{U}$ is much smaller than the number of projections and we can use a matrix factorization form $\bm{U}=\bm{L}\bm{R}$ for $\bm{U}$. The number of columns for the matrix $\bm{L}$ constraints the rank of $\bm{U}$ and hence implicitly imposing a temporal coherence condition among all the images in cine-CBCT. The desired image properties in $\bm{L}$ and the periodicity of the breathing pattern are achieved by penalizing the sparsity of the tight wavelet frame transform of $\bm{L}$ and that of the Fourier transform of $\bm{R}$, respectively. A split Bregman method is used to solve the problem. In this paper we focus on presenting this new algorithm and showing the proof of principle using simulation studies on an NCAT phantom.
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