A SURVEY OF
INVERSE METHODOLOGIES, META-EVOLUTIONARY OPTIMIZATION
AND BAYESIAN STATISTICS: APPLICATIONS TO In Vivo MRS
Ales Gottvald
Group of Inverse & Optimization Methodologies,
Institute of Scientific Instruments, Academy of Sciences of the CR,
Kralovopolska 147, CZ-612 64 Brno, Czech Republic
E-MAIL: gott@ISIBrno.cz
ABSTRACT: Inverse problems arise from ill-posed mappings in many areas of
science and engineering. For every inverse problem, there exist
some fundamental statistical limits for the accuracy of solutions.
These theoretical limits cannot be superseded in any way without incorporating
some additional prior information. A major "secret" of inversion methodologies consists
in identifying and applying all forms of prior information available,
both hidden and explicit. Meta-Evolutionary optimization and
Bayesian Statistics are central concepts behind a very general
inversion methodology recently developed. In this article, some
underlying ideas of this robust inversion methodology are reviewed.
As illustrated, uncertainty of the inversions may be reduced
by incorporating very general forms of prior information:
non-linear parametric models, probabilistic noise distributions,
deterministic constraint conditions, etc. This inversion
methodology is applied to an important problem from Magnetic Resonance Spectroscopy (MRS):
quantitative In Vivo MRS beyond inhomogeneity and noise limits. After analyzing the
principal role of prior information for solving inverse problems, some limitations of two
popular approaches (Sampled Pattern Matching, Artificial Neural Networks) are elucidated
as well.
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