Volume 34, pp. 163-169, 2008-2009.

Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach

Marco Paluszny, Miguel Martín-Landrove, Giovanni Figueroa, and Wuilian Torres

Abstract

An algebraic method is proposed to solve the inverse interpolation problem for data fitting by a linear combination of decaying exponentials. The method transforms the interpolation question into a problem of finding the roots of a single polynomial. The method is validated by numerical simulations using noiseless synthetic data with excellent results. The method is applied to medical data coming from magnetic resonance images of tumoral lesions in brain to obtain relaxation rate distribution functions, with results that are trustworthy and fast when compared with inverse Laplace methods.

Full Text (PDF) [235 KB]

Key words

de Prony's method, continuation methods, Gröbner bases, exponential equations, polynomial equations, nonlinear algebraic equations.

AMS subject classifications

15A15, 15A09, 15A23

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