Niu Shanzhou, Yu Gaohang, Ma Jianhua, Wang Jing
Department of Radiation Oncology, University of Texas Southwestern Medical Center, Dallas, TX 75235, USA.
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China.
Inverse Probl. 2018 Feb;34(2). doi: 10.1088/1361-6420/aa942c. Epub 2018 Jan 10.
Spectral computed tomography (CT) has been a promising technique in research and clinic because of its ability to produce improved energy resolution images with narrow energy bins. However, the narrow energy bin image is often affected by serious quantum noise because of the limited number of photons used in the corresponding energy bin. To address this problem, we present an iterative reconstruction method for spectral CT using nonlocal low-rank and sparse matrix decomposition (NLSMD), which exploits the self-similarity of patches that are collected in multi-energy images. Specifically, each set of patches can be decomposed into a low-rank component and a sparse component, and the low-rank component represents the stationary background over different energy bins, while the sparse component represents the rest of different spectral features in individual energy bins. Subsequently, an effective alternating optimization algorithm was developed to minimize the associated objective function. To validate and evaluate the NLSMD method, qualitative and quantitative studies were conducted by using simulated and real spectral CT data. Experimental results show that the NLSMD method improves spectral CT images in terms of noise reduction, artifacts suppression and resolution preservation.
光谱计算机断层扫描（CT）由于能够生成具有窄能量 bins 的改进能量分辨率图像，在研究和临床中一直是一种很有前景的技术。然而，由于在相应能量 bin 中使用的光子数量有限，窄能量 bin 图像常常受到严重量子噪声的影响。为了解决这个问题，我们提出了一种用于光谱 CT 的迭代重建方法，即使用非局部低秩和稀疏矩阵分解（NLSMD），该方法利用了在多能量图像中收集的块的自相似性。具体而言，每组块可以分解为一个低秩分量和一个稀疏分量，低秩分量表示不同能量 bin 上的平稳背景，而稀疏分量表示各个能量 bin 中不同光谱特征的其余部分。随后，开发了一种有效的交替优化算法来最小化相关的目标函数。为了验证和评估 NLSMD 方法，使用模拟和真实光谱 CT 数据进行了定性和定量研究。实验结果表明，NLSMD 方法在降噪、伪影抑制和分辨率保持方面改善了光谱 CT 图像。
