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[BBC10] A global optimization method using a random walk on a topological map and local variational inversions
Revue Internationale avec comité de lecture : Journal Inverse Problems, vol. 26(125011), pp. 17, 2010, (doi:10.1088/0266-5611/26/12/125011)
motcle:
Résumé:
This paper presents an improved variational method suitable for inverting a
problem associated with integral constrains. The method allows a global
minimization. We minimized a cost function representing the mismatch
between the measurements and the output of a numerical model, to which
we added a restoring term to a background. A way to process the covariance
matrix associated with the above-weighted quadratic background is to model
the control vectors using probabilistic principal component analysis (PPCA).
The use of PPCA presents difficulties in the case of a large dataset representing
the overall variability of the control space. We therefore developed a method
based on a topological map model, which allows partition of the dataset into
subsets more suited to the PPCA approach and thus leading to a local inversion
by the variational method. A random walk based on a Markov chain was
used to find the most appropriate subsets of the topological map by taking
into account a priori information on the unknown vector. This random walk
on a topological map allows us to reduce the number of subsets able to give
the optimal solution and thus to achieve a better performance at a lower cost.
An example of the application of this method to the shallow water acoustic
tomography inverse problem, showing its effectiveness, is presented.
Equipe:
msdma
Collaboration:
UPMC
BibTeX
| @article { | |||
| BBC10, | |||
| title | = | "{A global optimization method using a random walk on a topological map and local variational inversions}", | |
| author | = | "M. Berrada and F. Badran and M. Crépon and S. Thiria", | |
| journal | = | "Inverse Problems", | |
| year | = | 2010, | |
| volume | = | 26, | |
| number | = | 125011, | |
| pages | = | "17", | |
| doi | = | "10.1088/0266-5611/26/12/125011", | |
| } | |||
