We consider reconstructing multi-channel images from measurements performed by photon-counting and energy-discriminating detectors in the setting of multi-spectral X-ray computed tomography (CT). Our aim is to exploit the strong structural correlation that is known to exist between the channels of multi-spectral CT images. To that end, we adopt the multi-channel Potts prior to jointly reconstruct all channels. This prior produces piecewise constant solutions with strongly correlated channels. In particular, edges are enforced to have the same spatial position across channels which is a benefit over TV-based methods. We consider the Potts prior in two frameworks: (a) in the context of a variational Potts model, and (b) in a Potts-superiorization approach that perturbs the iterates of a basic iterative least squares solver. We identify an alternating direction method of multipliers (ADMM) approach as well as a Potts-superiorized conjugate gradient method as particularly suitable. In numerical experiments, we compare the Potts prior based approaches to existing TV-type approaches on realistically simulated multi-spectral CT data and obtain improved reconstruction for compound solid bodies.

中文翻译：

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基于多通道 Potts 的多光谱计算机断层扫描重建

我们考虑从多光谱 X 射线计算机断层扫描 (CT) 设置中的光子计数和能量鉴别探测器执行的测量中重建多通道图像。我们的目标是利用已知存在于多光谱 CT 图像通道之间的强结构相关性。为此，我们在联合重建所有通道之前采用多通道 Potts。该先验产生具有强相关通道的分段常数解。特别是，边缘被强制在频道间具有相同的空间位置，这比基于电视的方法更有优势。我们在两个框架中考虑 Potts 先验：（a）在变分 Potts 模型的上下文中，以及（b）在扰乱基本迭代最小二乘求解器的迭代的 Potts-superiorization 方法中。我们认为乘法器的交替方向方法 (ADMM) 方法以及 Potts 超优共轭梯度方法特别合适。在数值实验中，我们将基于 Potts 先验的方法与现实模拟的多光谱 CT 数据上的现有 TV 类型方法进行比较，并获得复合固体的改进重建。