PART 1: EVOLUTION STRATEGIES
Abstract: Evolution Strategy (ES) is a stochastic optimization method inspired by a biological evolution theory. It is a component of a general methodology elaborated for solving a large class of inverse and optimization problems in Magnetic Resonance and many other applications. We describe the ES in a context of some other stochastic optimization methods (Simulated Annealing, Genetic Algorithm). A concept of Meta-optimization is suggested for enforcing global convergence, eliminating parametric sensitivity, etc., of the standard ES.
Abstract: Meta-optimization means optimizing optimization itself. It is a fundamental concept behind a general methodology developed for solving a large class of inverse and optimization problems in Magnetic Resonance and many other applications. Some essential consequences of the Meta-optimization are: enforced global convergence, reduced parametric sensitivity, and total accuracy estimates. In this article, the principle of Meta-optimization is formulated and a Meta-Evolutionary algorithm "GNOME" is presented.
Abstract: Superconductive magnets, shim and gradient coils, rf-excitations and, especially, spectra quantifications state a large class of inverse and optimization problems in MR. Conventionally, these problems are treated as isolated topics prone to heuristic formulations and techniques. As indicated in this paper, modern methods including Evolution Strategies and Meta-optimization permit solving these inverse and optimization tasks from a general stand-point, where large portions of associated theory and software overlap.
Abstract: An inverse methodology is outlined that reduces two fundamental limitations of contemporary Magnetic Resonance Spectroscopy (MRS), namely homogeneity and noise restrictions. As an expected consequence, MRS can be generalized for a large class of experiments beyond contemporary homogeneity and noise limits. Moreover, both deterministic and probabilistic prior information may be utilized, and total accuracy estimates may be constructed. An impact on biomedical aplications of in vivo MRS can be expected. Significant cost reduction implications for some MR-devices, especially superconductive magnet systems, are very likely.
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