Deep Decomposition for Stochastic Normal-Abnormal Transport

TL;DR

This paper introduces D^2-SONATA, a machine learning model that decomposes transport processes into normal and abnormal components using stochastic advection-diffusion equations, with applications in medical imaging for stroke detection.

Contribution

The paper presents a novel deep learning framework that isolates abnormal transport behavior in stochastic advection-diffusion processes, enhancing medical diagnosis capabilities.

Findings

Successfully distinguishes stroke lesions from normal brain regions.

Accurately reconstructs velocity and diffusion tensor fields.

Demonstrates improved abnormality detection in transport data.

Abstract

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.