A Combinatorial Algorithm in Multiexponential Analysis

Alexander A. Roytvarf

A chapter in Thinking in Problems, 2013, pp 29-35 from Springer

Abstract: Abstract Deciphering, or multiexponential analysis of signals in a nuclear magnetic resonance (NMR) machine, is necessary for a composite analysis (e.g., for separating oil fractions in well logging, detecting affected tissue in medicine). NMR signals are modeled by functions of the form $$ f(x)=\sum {{A_i}{e^{{{\omega_i}x}}}} $$ , which are linear combinations of exponential terms; in these f, the parameters ω i correspond to different components, and A i characterize their relative weights in the composite. The number, and value of the parameters A i and ω i are not known, and so the multiexponential analysis consists in determining them (within some tolerance); this analysis relates to so-called inverse problems, usually characterized by a high degree of instability. This chapter contains real-life algebraic and combinatorial problems that arose in the development of a stable algorithm for multiexponential analysis.

Keywords: Multiexponential Analysis; Exponential Term; Stable Algorithm; Itskovich; Total Relative Contribution (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8406-8_3

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DOI: 10.1007/978-0-8176-8406-8_3

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