ON DIRECT ALGEBRAIC IDENTIFICATION OF INHOMOGENEITY FUNCTIONS IN MRS
Hana Kucharova, Ales Gottvald
Institute of Scientific Instruments, Academy of Sciences of the CR,
Kralovopolska 147, CZ-612 64 Brno, Czech Republic
E-mail: hanca@isibrno.cz, gott@isibrno.cz
Internet: http://www.isibrno.cz/~hanca/index.html, ../~gott/index.html
with pseudo-math symbols
Abstract: Inhomogeneity functions w(t) and W(v) := F[w(t)] are major
structures for incorporating inhomogeneity phenomena into qualitative and quantitative
analysis of experimental data in MR-Spectroscopy. Identification of the inhomogeneity
functions is a natural generalization of conventional "shimming" or "tuning" operations
well known to every MR-spectroscopist. Some non-Fourier quantification methodologies in
MRS are intrinsically capable of incorporating any inhomogeneity function. Hence, various
inhomogeneity phenomena may be separated from the signals and the spectra. Being given a
reference FID-signal and an identification FID-signal, the inhomogeneity function may be
identified directly from experimental data. Direct Algebraic Identification (DAI)
comprises the simplest non-parametric method of determining the cartesian components,
modules and phases of inhomogeneity functions. Using real-world experimental data, we
verified that DAI works properly for singlets with sufficiently low noise and phase
distortions. For multiplets with some stronger noise and phase distortions, DAI is
prone to artifacts, though some useful results may be still obtained in many practical
cases.
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