用于可微图像配准的分解Levenberg-Marquardt：FireANTs的高效优化器

FireANTs introduces a novel Eulerian descent method for plug-and-play behavior tailored for diffeomorphic image registration, treating it as a test-time optimization problem with a GPU-accelerated implementation. The default optimizer used by FireANTs is Adam, which allows for fast and robust optimization. However, Adam's requirement to store state variables, such as momentum and squared-momentum estimates, can lead to significant memory consumption, limiting its applicability for large images. A modified Levenberg-Marquardt (LM) optimizer is proposed, which requires only a single scalar damping parameter as optimizer state, adaptively tuned using a trust region approach. This results in a memory reduction of up to 24%, making it feasible for larger image processing tasks.