Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration

• URL: http://arxiv.org/abs/2109.12688v1
• Date: Sun, 26 Sep 2021 19:56:45 GMT
• Title: Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration
• Authors: Alexander Thorley, Xi Jia, Hyung Jin Chang, Boyang Liu, Karina Bunting, Victoria Stoll, Antonio de Marvao, Declan P. O'Regan, Georgios Gkoutos, Dipak Kotecha, Jinming Duan
• Abstract summary: Recent developments in approaches based on deep learning have achieved sub-second runtimes for DiffIR. We propose a simple iterative scheme that functionally composes intermediate non-stationary velocity fields. We then propose a convex optimisation model that uses a regularisation term of arbitrary order to impose smoothness on these velocity fields.
• Score: 63.15453821022452
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deterministic approaches using iterative optimisation have been historically successful in diffeomorphic image registration (DiffIR). Although these approaches are highly accurate, they typically carry a significant computational burden. Recent developments in stochastic approaches based on deep learning have achieved sub-second runtimes for DiffIR with competitive registration accuracy, offering a fast alternative to conventional iterative methods. In this paper, we attempt to reduce this difference in speed whilst retaining the performance advantage of iterative approaches in DiffIR. We first propose a simple iterative scheme that functionally composes intermediate non-stationary velocity fields to handle large deformations in images whilst guaranteeing diffeomorphisms in the resultant deformation. We then propose a convex optimisation model that uses a regularisation term of arbitrary order to impose smoothness on these velocity fields and solve this model with a fast algorithm that combines Nesterov gradient descent and the alternating direction method of multipliers (ADMM). Finally, we leverage the computational power of GPU to implement this accelerated ADMM solver on a 3D cardiac MRI dataset, further reducing runtime to less than 2 seconds. In addition to producing strictly diffeomorphic deformations, our methods outperform both state-of-the-art deep learning-based and iterative DiffIR approaches in terms of dice and Hausdorff scores, with speed approaching the inference time of deep learning-based methods.

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