# Learning-based Ensemble Average Propagator Estimation

## TL;DR

This paper introduces LEAPE, a deep learning method for estimating the ensemble average propagator in diffusion MRI, improving accuracy with limited clinical data by leveraging a specialized neural network architecture.

## Contribution

The paper presents a novel deep learning framework that estimates EAP coefficients using a cascaded neural network with geometry-aware regularization, enhancing clinical applicability.

## Key findings

- LEAPE outperforms conventional methods in accuracy.
- The method effectively estimates fiber orientations.
- Promising results with clinically feasible data sampling.

## Abstract

By capturing the anisotropic water diffusion in tissue, diffusion magnetic resonance imaging (dMRI) provides a unique tool for noninvasively probing the tissue microstructure and orientation in the human brain. The diffusion profile can be described by the ensemble average propagator (EAP), which is inferred from observed diffusion signals. However, accurate EAP estimation using the number of diffusion gradients that is clinically practical can be challenging. In this work, we propose a deep learning algorithm for EAP estimation, which is named learning-based ensemble average propagator estimation (LEAPE). The EAP is commonly represented by a basis and its associated coefficients, and here we choose the SHORE basis and design a deep network to estimate the coefficients. The network comprises two cascaded components. The first component is a multiple layer perceptron (MLP) that simultaneously predicts the unknown coefficients. However, typical training loss functions, such as mean squared errors, may not properly represent the geometry of the possibly non-Euclidean space of the coefficients, which in particular causes problems for the extraction of directional information from the EAP. Therefore, to regularize the training, in the second component we compute an auxiliary output of approximated fiber orientation (FO) errors with the aid of a second MLP that is trained separately. We performed experiments using dMRI data that resemble clinically achievable $q$-space sampling, and observed promising results compared with the conventional EAP estimation method.