Automatic Hyperparameter Tuning in Physics-Based Distortion Correction for Diffusion Tensor Imaging Open Access
Julian, Abigail (Spring 2024)
Published
Abstract
Correction of susceptibility artifacts in Echo-Planar Imaging (EPI) is a computationally challenging problem due to its size, non-linearity, and scarcity of ground truth data. Although several post-processing tools for three-dimensional EPI distortion correction are available, these tools require choosing hyperparameters and are often slow, taking several minutes per image volume. In this dissertation, we develop a dependable, physics-based correction with automatic hyperparameter tuning in the context of Diffusion Tensor Imaging (DTI).
First, we build upon existing tools to solve the three-dimensional distortion correction problem in a matter of seconds using a separable optimization setup and highly parallelizable implementation. We implement an early one-dimensional correction approach as an initialization scheme using one-dimensional optimal transport, and implement an easy-to-use PyTorch tool that enables multi-threading and efficient use of graphics processing units (GPUs). Our extensive numerical validation using 3T and 7T data from the Human Connectome Project suggests that our tool achieves accuracy comparable to that of leading distortion correction tools at a fraction of the cost. We also validate the initialization scheme, compare different optimization algorithms, and test the algorithm on different hardware and arithmetic precision.
Second, we expand distortion correction to four-dimensional DTI volumes. In this setting, the three-dimensional brain volume is repeatedly imaged with a different diffusion gradient applied. Using the scalable initialization and optimization setup from the three-dimensional setting, we optimize in 4D using a parameterization of the additional diffusion dimension, leveraging the additional information offered by the associated directions of diffusion. We test a variety of parameterizations that relate the diffusion directions and introduce smoothness in the diffusion dimension. We also employ clustering to choose a subset of directions for optimization, and use the parameterization to interpolate on the original volume containing all of the diffusion directions.
Third and finally, we enable automatic hyperparameter tuning, possible because of the efficiency of four-dimensional distortion correction. We set up a bilevel optimization using metrics of DTI to tune the hyperparameters of the distortion correction problem. The resulting tool runs in times comparable to existing correction tools while not requiring the user to select any hyperparameters. Furthermore, the correction is dependable, since it is based on the interpretable physics of the distortion, and the correction simultaneously optimizes the metrics of the downstream task, diffusion tensor fit.
Table of Contents
Chapter 1: Introduction ............................... 1
1.1 Contributions ............................... 3
1.2 Overview............................... 5
Chapter 2: Background and Preliminaries............................... 6
2.1 Reversed Gradient Polarity Correction ............................... 6
2.2 Susceptibility Artifact Distortion Correction Model............................... 9
2.3 Separable Optimization Problem............................... 9
2.4 Optimization Schemes ............................... 12
2.5 Diffusion Tensor Imaging............................... 17
2.6 Bilevel and Derivative-Free Optimization................................ 19
Chapter 3: GPU-Enabled 3D Distortion Correction in Seconds............................... 22
3.1 Parallelized One-Dimensional Initialization............................... 23
3.2 Parallelized Optimization............................... 26
3.3 PyHySCO: A GPU-Enabled, Command Line Compatible, PyTorch Correction Tool............................... 28
3.4 Results................................ 34
3.5 Summary............................... 42
Chapter 4: Parameterized Four-Dimensional DTI Correction............................... 52
4.1 Four-Dimensional Optimization Problem ............................... 53
4.2 Field Map Parameterizations............................... 55
4.3 Cluster, Reduce, Optimize, and Interpolate............................... 63
4.4 Results............................... 65
4.5 Summary............................... 82
Chapter 5: Automatic Hyperparameter Tuning............................... 84
5.1 L-curve Analysis............................... 85
5.2 Bilevel Optimization............................... 86
5.3 Results................................ 87
5.4 Summary............................... 94
Chapter 6: Conclusion............................... 96
Bibliography............................... 98
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