# [BBT08] Probabilistic PCA and Ocean Acoustic Tomography inversion with an adjoint method

**Atelier, Poster ou Démonstration dans une Conférence Internationale : **
Acoustics'08, ASA EAA SFA,
January 2008,

pp.xx,

**motcle: **

**Résumé: **
We present an Ocean Acoustic Tomography (OAT) inversion in a shallow water environment. The idea is to determine the celerity $c(z),\;z$ is depth, knowing the acoustic pressures caused by a multiple frequencies source and collected by a sparse receiver array. The variational approach minimizes a cost function which measures the adequacy between the measurements and their forward model equivalent. This method introduces also a regularization term in the form $(c(z)-c_b(z))^TB^{-1}(c(z)-c_b(z))$, which supposes that $c(z)$ follows an \textit{a priori} normal law. To circumvent the problem of estimating $B^{-1},$ we propose to model the celerity vectors by a probabilistic PCA. In contrast to the methods which use PCA as a regularization method and filter the useful information, we take a sufficient number of axes which allow the modelization of useful information and filter only the noise. The probabilistic PCA introduces a reduced number of non correlated latent variables $\eta$ which act as new control parameters introduced in the cost function. This new regularization term, expressed as $\eta^T\eta,$ reduces the optimization computation time. In the following we apply the probabilistic PCA to an OAT problem, and present the results obtained when performing twin experiments.

**Commentaires: **
Paris, June 29- July 4

Collaboration:
UPMC