论文标题
联合重建和动态逆问题的低排时分解
Joint Reconstruction and Low-Rank Decomposition for Dynamic Inverse Problems
论文作者
论文摘要
动态反问题的主要兴趣是从外部测量值中确定系统的潜在时间行为。在这项工作中，我们考虑了该案例，即目标可以通过空间和时间基础函数的分解来表示，因此可以通过低级别分解有效地表示。然后，我们提出了基于非负矩阵分解的联合重建和低级分解方法，以从高度不足的动态测量数据中获得未知数。所提出的框架允许灵活地掺入空间和时间特征的单独的正规机构。对于固定操作员的特殊情况，我们可以有效地使用分解来降低计算复杂性并获得大量加速。评估了两个模拟幻象的提议方法，我们将获得的结果与基于广泛使用的主成分分析的单独的低级别重建方法和随后的分解方法进行了比较。
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial and temporal basis functions and hence can be efficiently represented by a low-rank decomposition. We then propose a joint reconstruction and low-rank decomposition method based on the Nonnegative Matrix Factorisation to obtain the unknown from highly undersampled dynamic measurement data. The proposed framework allows for flexible incorporation of separate regularisers for spatial and temporal features. For the special case of a stationary operator, we can effectively use the decomposition to reduce the computational complexity and obtain a substantial speed-up. The proposed methods are evaluated for two simulated phantoms and we compare the obtained results to a separate low-rank reconstruction and subsequent decomposition approach based on the widely used principal component analysis.
