A Comparison of Gradient-Based Optimization Techniques in Magnetic Resonance Elastography

Magnetic Resonance Elastography (MRE) involves the solution of an inverse problem as a PDE-constrained optimization problem to determine the unknown material model parameters by utilizing the full-field displacement data. Levenberg–Marquardt (LM) within the Gauss–Newton’s methods and Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm within the Quasi-Newton methods are the two most commonly used gradient-based optimization techniques for solving the inverse problem of MRE. A comparison between their performance and efficiency is lacking in the literature. The present study demonstrates the application of these two techniques for solving the inverse problem. A two-dimensional linear elastic boundary value problem under plane strain condition was considered for generating the synthetic displacement field data for the MRE. The performance of both LM and BFGS algorithms has been compared based on metrics such as accuracy, convergence, and computation cost. It has been observed that LM converges faster than the BFGS method with higher reconstruction accuracy. However, as the number of model parameters increases, the computational cost associated with the LM method significantly outweighs that of the BFGS method. An alternative strategy based on the sub-domain approach coupled with the LM method demonstrated high efficacy, even for a large number of model parameters. The proposed approach can also be deployed to large-scale optimization problems in other engineering domains.