Gauss-Newton inspired preconditioned optimization in large deformation diffeomorphic metric mapping

Area of Science:

• Medical Imaging
• Computer Vision
• Computational Anatomy

Background:

• Non-rigid image registration is crucial for medical image analysis.
• Large Deformation Diffeomorphic Metric Mapping (LDDMM) is a powerful framework for this task.
• Existing LDDMM methods often rely on computationally intensive gradient descent optimization.

Purpose of the Study:

• To introduce a novel preconditioned optimization method for LDDMM.
• To enhance the computational efficiency and accuracy of LDDMM-based image registration.
• To compare the performance of the proposed methods against gradient descent approaches.

Main Methods:

• Formulated preconditioned update schemes for both stationary and non-stationary LDDMM parameterizations.
• Developed preconditioning matrices inspired by Gauss-Newton Hessian approximations.
• Employed Frechet differentials for derivative computation, optimizing within a Sobolev space.

Main Results:

• The proposed preconditioned LDDMM methods achieved performance comparable or superior to gradient descent LDDMM.
• Demonstrated a substantial reduction in execution time with only a modest increase in memory usage.
• Validated findings using real and simulated image data from the NIREP dataset.

Conclusions:

• Preconditioned optimization offers a more efficient and effective approach for LDDMM.
• Optimization using Frechet differentials is preferable to L(2) differentials for non-rigid registration.
• The novel LDDMM methods provide a valuable advancement for medical image analysis applications.