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.

中文翻译：

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谱CT重建的非局部低秩稀疏矩阵分解

光谱计算机断层扫描 (CT) 已成为研究和临床中一种很有前途的技术，因为它能够产生具有窄能量区间的改进的能量分辨率图像。然而，由于相应能量仓中使用的光子数量有限，窄能量仓图像往往受到严重量子噪声的影响。为了解决这个问题，我们提出了一种使用非局部低秩稀疏矩阵分解 (NLSMD) 的光谱 CT 迭代重建方法，该方法利用了多能量图像中收集的补丁的自相似性。具体来说，每组补丁可以分解为一个低秩分量和一个稀疏分量，低秩分量代表不同能量仓上的平稳背景，而稀疏分量表示各个能量箱中的其余不同光谱特征。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。