We consider the solution of inverse problems in dynamic contrast–enhanced imaging by means of Ensemble Kalman Filters. Our quantity of interest is blood perfusion, i.e. blood flow rates in tissue. While existing approaches to compute blood perfusion parameters for given time series of radiological measurements mainly rely on deterministic, deconvolution–based methods, we aim at recovering probabilistic solution information for given noisy measurements. To this end, we model radiological image capturing as sequential data assimilation process and solve it by an Ensemble Kalman Filter. Thereby, we recover deterministic results as ensemble–based mean and are able to compute reliability information such as probabilities for the perfusion to be in a given range. Our target application is the inference of blood perfusion parameters in the human brain. A numerical study shows promising results for artificial measurements generated by a Digital Perfusion Phantom.

中文翻译：

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用于灌注推断中可靠性估计的集成卡尔曼滤波器

我们考虑通过集成卡尔曼滤波器解决动态对比度增强成像中的逆问题。我们感兴趣的数量是血液灌注，即组织中的血液流速。虽然为给定的放射测量时间序列计算血液灌注参数的现有方法主要依赖于确定性的、基于反卷积的方法，但我们的目标是为给定的噪声测量恢复概率解信息。为此，我们将放射图像捕获建模为连续数据同化过程，并通过集成卡尔曼滤波器对其进行求解。因此，我们将确定性结果恢复为基于集合的平均值，并且能够计算可靠性信息，例如灌注在给定范围内的概率。我们的目标应用是推断人脑中的血液灌注参数。