Geodesic
Data completion and stochastic algorithms for PDE inversion problems with many measurements
Electronic transactions on numerical analysis, Tome 42 (2014), pp. 177-196.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. Assuming that all experiments share the same set of receivers, in a recent paper we examined both stochastic and deterministic dimensionality reduction methods to reduce this computational burden. In the present article we consider the more general and practically important case where receivers are not shared across experiments. We propose a data completion approach to alleviate this problem. This is done by means of an approximation using an appropriately restricted gradient or Laplacian regularization, extending existing data for each experiment to the union of all receiver locations. Results using the method of simultaneous sources (SS) with the completed data are then compared to those obtained by a more general but slower random subset (RS) method which requires no modifications.
Classification : 65N21, 65C05
Keywords: stochastic algorithm, data completion, inverse problem, partial differential equation, many experiments, DC resistivity 
@article{ETNA_2014__42__a0,
     author = {Roosta-Khorasani, Farbod and van den Doel, Kees and Ascher, Uri},
     title = {Data completion and stochastic algorithms for {PDE} inversion problems with many measurements},
     journal = {Electronic transactions on numerical analysis},
     pages = {177--196},
     publisher = {mathdoc},
     volume = {42},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__42__a0/}
}
TY  - JOUR
AU  - Roosta-Khorasani, Farbod
AU  - van den Doel, Kees
AU  - Ascher, Uri
TI  - Data completion and stochastic algorithms for PDE inversion problems with many measurements
JO  - Electronic transactions on numerical analysis
PY  - 2014
SP  - 177
EP  - 196
VL  - 42
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_2014__42__a0/
LA  - en
ID  - ETNA_2014__42__a0
ER  - 
%0 Journal Article
%A Roosta-Khorasani, Farbod
%A van den Doel, Kees
%A Ascher, Uri
%T Data completion and stochastic algorithms for PDE inversion problems with many measurements
%J Electronic transactions on numerical analysis
%D 2014
%P 177-196
%V 42
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_2014__42__a0/
%G en
%F ETNA_2014__42__a0
Roosta-Khorasani, Farbod; van den Doel, Kees; Ascher, Uri. Data completion and stochastic algorithms for PDE inversion problems with many measurements. Electronic transactions on numerical analysis, Tome 42 (2014), pp. 177-196. http://geodesic.mathdoc.fr/item/ETNA_2014__42__a0/