基于ADMM的谱分组总变分重建用于散射成像
Spectrally Grouped Total Variation Reconstruction for Scatter Imaging Using ADMM
AI总结：
本文提出基于ADMM的谱分组总变分重建算法，通过改进的正则化方法提升散射成像的谱与空间质量，利用凸分解实现并行优化。
摘要：
我们考虑X射线相干散射成像，目标是从多重散射测量中重建每个空间位置的动量转移分布（谱分布）。每种材料具有独特的动量转移分布（MTP），可用于区分不同材料。我们提出了一种基于泊松噪声模型的迭代图像重建算法，能够处理光子限制的测量以及数据的多种二次统计。为了提高图像质量，先前方法使用边缘保持正则化器以在空间域中促进分段常数图像，而每个谱bin分别处理。相反，我们提出谱分组正则化，促进空间方向上的分段常数图像，同时确保相邻空间bin的MTP相似，如果它们包含相同材料。我们证明这种分组正则化在谱和空间图像质量上都有提升。我们追求一种优化转移方法，利用凸分解将问题提升，使得所有超体素可以并行更新并以闭式形式处理。分组惩罚引入了挑战，因为它不直接适用于这些分解。我们使用交替方向乘子法（ADMM）将原问题替换为一个等效的子问题序列，这些子问题适用于凸分解，导致高度并行的算法。我们在真实数据上展示了性能。
英文摘要：
We consider X-ray coherent scatter imaging, where the goal is to reconstruct momentum transfer profiles (spectral distributions) at each spatial location from multiplexed measurements of scatter. Each material is characterized by a unique momentum transfer profile (MTP) which can be used to discriminate between different materials. We propose an iterative image reconstruction algorithm based on a Poisson noise model that can account for photon-limited measurements as well as various second order statistics of the data. To improve image quality, previous approaches use edge-preserving regularizers to promote piecewise constancy of the image in the spatial domain while treating each spectral bin separately. Instead, we propose spectrally grouped regularization that promotes piecewise constant images along the spatial directions but also ensures that the MTPs of neighboring spatial bins are similar, if they contain the same material. We demonstrate that this group regularization results in improvement of both spectral and spatial image quality. We pursue an optimization transfer approach where convex decompositions are used to lift the problem such that all hyper-voxels can be updated in parallel and in closed-form. The group penalty introduces a challenge since it is not directly amendable to these decompositions. We use the alternating directions method of multipliers (ADMM) to replace the original problem with an equivalent sequence of sub-problems that are amendable to convex decompositions, leading to a highly parallel algorithm. We demonstrate the performance on real data.
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