Spectral computed tomography (CT) reconstructs the same scanned object from projections of multiple narrow energy windows, and it can be used for material identification and decomposition. However, the multi-energy projection dataset has a lower signal-noise-ratio (SNR), resulting in poor reconstructed image quality. To address this thorny problem, we develop a spectral CT reconstruction method, namely spatial-spectral cube matching frame (SSCMF). This method is inspired by the following three facts: i) human body usually consists of two or three basic materials implying that the reconstructed spectral images have a strong sparsity; ii) the same basic material component in a single channel image has similar intensity and structures in local regions. Different material components within the same energy channel share similar structural information; iii) multi-energy projection datasets are collected from the subject by using different narrow energy windows, which means images reconstructed from different energy-channels share similar structures. To explore those information, we first establish a tensor cube matching frame (CMF) for a BM4D denoising procedure. Then, as a new regularizer, the CMF is introduced into a basic spectral CT reconstruction model, generating the SSCMF method. Because the SSCMF model contains an L0-norm minimization of 4D transform coefficients, an effective strategy is employed for optimization. Both numerical simulations and realistic preclinical mouse studies are performed. The results show that the SSCMF method outperforms the state-of-the-art algorithms, including the simultaneous algebraic reconstruction technique, total variation minimization, total variation plus low rank, and tensor dictionary learning.

中文翻译：

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用于能谱 CT 重建的空间能谱立方匹配框架

光谱计算机断层扫描 (CT) 通过多个窄能量窗的投影重建同一扫描对象，可用于材料识别和分解。然而，多能量投影数据集的信噪比（SNR）较低，导致重建图像质量较差。为了解决这个棘手的问题，我们开发了一种光谱CT重建方法，即空间光谱立方匹配框架（SSCMF）。该方法受到以下三个事实的启发：i）人体通常由两种或三种基本材料组成，这意味着重建的光谱图像具有很强的稀疏性；ii）单通道图像中相同的基本材料成分在局部区域具有相似的强度和结构。同一能量通道内的不同物质成分共享相似的结构信息；iii）多能量投影数据集是通过使用不同的窄能量窗口从受试者收集的，这意味着从不同能量通道重建的图像具有相似的结构。为了探索这些信息，我们首先为 BM4D 去噪过程建立张量立方体匹配框架 (CMF)。然后，将CMF作为一种新的正则化器引入到基本的能谱CT重建模型中，生成SSCMF方法。由于 SSCMF 模型包含 4D 变换系数的 L0 范数最小化，因此采用了有效的优化策略。进行了数值模拟和现实的临床前小鼠研究。结果表明，SSCMF 方法优于最先进的算法，包括同时代数重构技术、总变分最小化、总变分加低秩和张量字典学习。