Geodesic
Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach
Electronic transactions on numerical analysis, Tome 34 (2009)
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.
Classification : 15A15, 15A09, 15A23
Keywords: de prony's method, continuation methods, gr$\ddot $obner bases, exponential equations, polynomial equations, nonlinear algebraic equations 
@article{ETNA_2009__34__a2,
     author = {Paluszny,  Marco and Mart{\'\i}n-Landrove,  Miguel and Figueroa,  Giovanni and Torres,  Wuilian},
     title = {Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach},
     journal = {Electronic transactions on numerical analysis},
     year = {2009},
     volume = {34},
     zbl = {1188.65073},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2009__34__a2/}
}
TY  - JOUR
AU  - Paluszny,  Marco
AU  - Martín-Landrove,  Miguel
AU  - Figueroa,  Giovanni
AU  - Torres,  Wuilian
TI  - Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach
JO  - Electronic transactions on numerical analysis
PY  - 2009
VL  - 34
UR  - http://geodesic.mathdoc.fr/item/ETNA_2009__34__a2/
LA  - en
ID  - ETNA_2009__34__a2
ER  - 
%0 Journal Article
%A Paluszny,  Marco
%A Martín-Landrove,  Miguel
%A Figueroa,  Giovanni
%A Torres,  Wuilian
%T Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach
%J Electronic transactions on numerical analysis
%D 2009
%V 34
%U http://geodesic.mathdoc.fr/item/ETNA_2009__34__a2/
%G en
%F ETNA_2009__34__a2
Paluszny,  Marco; Martín-Landrove,  Miguel; Figueroa,  Giovanni; Torres,  Wuilian. Boosting the inverse interpolation problem by a sum of decaying exponentials using an algebraic approach. Electronic transactions on numerical analysis, Tome 34 (2009). http://geodesic.mathdoc.fr/item/ETNA_2009__34__a2/