ADAPTIVE GRADIENT DESCENT OPTIMIZATION OF INITIAL MOMENTA FOR GEODESIC SHOOTING IN DIFFEOMORPHISMS

Area of Science:

• Medical Imaging
• Computational Anatomy
• Optimization Algorithms

Background:

• Diffeomorphic image registration is crucial in medical imaging, involving complex high-dimensional nonlinear objective function optimization.
• Current methods often use simple gradient descent without clear strategies for step size selection or line searches, limiting adaptability.
• Robustness to varying image inputs necessitates adaptable optimization schemes for accurate anatomical change quantification.

Purpose of the Study:

• To introduce and evaluate two adaptable gradient descent methods with line searches for diffeomorphic image registration.
• To assess the impact of these optimization schemes on convergence characteristics and the quantification of anatomical changes (atrophy).
• To determine the clinical significance of atrophy measurements derived from optimized registration, correlating with diagnostic groups and cognitive scores.

Main Methods:

• Implemented two adaptable gradient descent algorithms incorporating line searches.
• Deployed these optimization schemes within the geodesic shooting framework for diffeomorphic registration of longitudinal image pairs.
• Evaluated convergence speed, adaptability, and the correlation of calculated atrophy scores with clinical data (diagnostic group, Mini Mental State Exam scores).

Main Results:

• The Barzilai-Borwein method combined with a backtracking line search demonstrated superior performance in convergence time and adaptability compared to other tested schemes.
• Variable optimization schemes did not significantly alter the ability to measure atrophy with clinically relevant significance.
• The enhanced optimization methods showed promise for improving the efficiency of anatomical change analysis in medical imaging.

Conclusions:

• Adaptable gradient descent with line searches, particularly the Barzilai-Borwein method, offers significant advantages for optimizing diffeomorphic image registration.
• Efficient optimization can accelerate the analysis of anatomical changes from longitudinal medical images.
• The chosen optimization strategies maintain the clinical validity of atrophy measurements, supporting their use in diagnostic assessments.