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A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION
1The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, 78712-0027, US.
SIAM Journal on Scientific Computing : a Publication of the Society for Industrial and Applied Mathematics
|December 20, 2017
Summary
We developed a faster numerical algorithm for diffeomorphic image registration using advanced computational methods. This new approach significantly speeds up medical image analysis, achieving a 20x improvement in complex registration tasks.
Area of Science:
- Computational mathematics
- Medical imaging
- Image registration
Background:
- Diffeomorphic image registration is crucial for medical image analysis.
- Existing numerical methods can be computationally intensive.
- Efficient algorithms are needed to accelerate registration processes.
Purpose of the Study:
- To develop and evaluate an efficient numerical algorithm for solving diffeomorphic image registration problems.
- To improve computational speed and efficiency compared to previous implementations.
- To assess the algorithm's performance on synthetic and real-world medical imaging data.
Main Methods:
- Utilized a variational formulation constrained by a scalar transport partial differential equation (PDE).
- Employed pseudospectral discretization in space and a second-order semi-Lagrangian time-stepping scheme.
- Solved for a stationary velocity field using a preconditioned, matrix-free Newton-Krylov scheme with a two-level Hessian preconditioner.
- Investigated nested preconditioned conjugate gradient and Chebyshev iterative methods for coarse grid inversion.
Main Results:
- The proposed algorithm demonstrated significant speedups compared to the initial implementation.
- Achieved a 20x speedup for a 2D real-world multi-subject medical image registration problem.
- Showcased grid convergence and computational efficiency in various application scenarios.
Conclusions:
- The new numerical algorithm offers substantial computational advantages for diffeomorphic image registration.
- The efficient solver accelerates complex medical image analysis tasks.
- The method is robust and effective for both synthetic and real-world data.
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