Advection-diffusion equations describe a large family of natural transport processes, e.g., fluid flow, heat transfer, and wind transport. They are also used for optical flow and perfusion imaging computations. We develop a machine learning model, D^2-SONATA, built upon a stochastic advection-diffusion equation, which predicts the velocity and diffusion fields that drive 2D/3D image time-series of transport. In particular, our proposed model incorporates a model of transport atypicality, which isolates abnormal differences between expected normal transport behavior and the observed transport. In a medical context such a normal-abnormal decomposition can be used, for example, to quantify pathologies. Specifically, our model identifies the advection and diffusion contributions from the transport time-series and simultaneously predicts an anomaly value field to provide a decomposition into normal and abnormal advection and diffusion behavior. To achieve improved estimation performance for the velocity and diffusion-tensor fields underlying the advection-diffusion process and for the estimation of the anomaly fields, we create a 2D/3D anomaly-encoded advection-diffusion simulator, which allows for supervised learning. We further apply our model on a brain perfusion dataset from ischemic stroke patients via transfer learning. Extensive comparisons demonstrate that our model successfully distinguishes stroke lesions (abnormal) from normal brain regions, while reconstructing the underlying velocity and diffusion tensor fields.
翻译:振荡- 振荡- 振荡- 振荡- 振荡- 振荡- 振荡- 振荡- 振荡- 振动- 振动- 振动- 振动- 振动- 振动- 振动- 振动- 振动- 振动- 振动- 振动- 振动- 振动- 等方程式; 我们提议的模型包含一个运输非典型性模型,它将预期的正常运输行为和观察到的运输行为之间的异常差异隔开来。 在医学方面,还可以使用这种正常- 异常的分解方法来计算光流和充气流。 我们开发了一个机器学习模式D/3- 正常- 振动- 振动- 振动- 振动- 变异- 区域, 并同时预测一个异常的值字段,以提供正常和异常的振动- 振动- 振荡- 振动- 行为。为了提高模型的性- 振荡- 振动- 振动- 振动- 将我们的大脑- 振动- 系统- 学习到我们的大脑- 系统- 系统- 演示- 演示- 演示- 以 向- 演示- 向- 向- 向- 向- 模拟- 将- 将我们的大脑- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向- 向-