Assimilation of image sequences in numerical models

Abstract Understanding and forecasting the evolution of geophysical fluids is a major scientific and societal challenge. Forecasting algorithms should take into account all the available information on the considered dynamic system. The variational data assimilation (VDA) technique combines all these informations in an optimality system (O.S.) in a consistent way to reconstruct the model inputs. VDA is currently used by the major meteorological centres. During the last two decades about 30 satellites were launched to improve the knowledge of the atmosphere and of the oceans. They continuously provide a huge amount of data that are still underused by numerical forecast systems. In particular, the dynamic evolution of certain meteorological or oceanic features (such as eddies, fronts, etc.) that the human vision may easily detect is not optimally taken into account in realistic applications of VDA. Image Assimilation in VDA framework can be performed using ‘pseudo-observation’ techniques: they provide apparent velocity fields, which are assimilated as classical observations. These measurements are obtained by certain external procedures, which are decoupled with the considered dynamic system. In this paper, we suggest a more consistent approach, which directly incorporates image sequences into the O.S.

[1]  David Suter,et al.  Motion estimation and vector splines , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[2]  F. L. Dimet,et al.  Coupling models and data: Which possibilities for remotely-sensed images? , 2004 .

[3]  Jean Charles Gilbert,et al.  LIBOPT - An environment for testing solvers on heterogeneous collections of problems - Version 1.0 , 2007, ArXiv.

[4]  E. Candès,et al.  Ridgelets: a key to higher-dimensional intermittency? , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[5]  S. Mallat A wavelet tour of signal processing , 1998 .

[6]  I. Eames,et al.  Dynamics of monopolar vortices on a topographic beta-plane , 2002, Journal of Fluid Mechanics.

[7]  Bruno Luong,et al.  A variational method for the resolution of a data assimilation problem in oceanography , 1998 .

[8]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  J. Fehrenbach,et al.  Identification of velocity fields for geophysical fluids from a sequence of images , 2011 .

[10]  David J. Fleet,et al.  Performance of optical flow techniques , 1994, International Journal of Computer Vision.

[11]  Isabelle Herlin,et al.  ANALYSIS OF THE BLACK SEA SURFACE CURRENTS RETRIEVED FROM SPACE IMAGERY , 2007 .

[12]  F. L. Dimet,et al.  Vector field regularization by generalized diffusion , 2009 .

[13]  Nicolas Papadakis,et al.  A Variational Technique for Time Consistent Tracking of Curves and Motion , 2008, Journal of Mathematical Imaging and Vision.

[14]  Marc Honnorat Assimilation de données lagrangiennes pour la simulation numérique en hydraulique fluviale , 2007 .

[15]  M. Nodet,et al.  Modélisation mathématique et assimilation de données lagrangiennes pour l'océanographie , 2005 .

[16]  F. L. Dimet,et al.  Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects , 1986 .

[17]  R. Adrian Particle-Imaging Techniques for Experimental Fluid Mechanics , 1991 .

[18]  Gjlles Aubert,et al.  Mathematical problems in image processing , 2001 .

[19]  Francesco d'Ovidio,et al.  Stirring of the northeast Atlantic spring bloom: A Lagrangian analysis based on multisatellite data , 2007 .

[20]  Laurent Demanet,et al.  Fast Discrete Curvelet Transforms , 2006, Multiscale Model. Simul..

[21]  François-Xavier Le Dimet,et al.  Spatio-temporal structure extraction and denoising of geophysical fluid image sequences using 3D curvelet transforms , 2007 .

[22]  L. Amodei,et al.  A vector spline approximation , 1991 .

[23]  Isabelle Herlin,et al.  Data Assimilation of Satellite Images Within an Oceanographic Circulation Model , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[24]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[25]  Gerlind Plonka-Hoch,et al.  Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion , 2007, IEEE Transactions on Image Processing.

[26]  Isabelle Herlin,et al.  Fast and Stable Vector Spline Method for Fluid Apparent Motion Estimation , 2007, 2007 IEEE International Conference on Image Processing.

[27]  E. Candès,et al.  New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities , 2004 .

[28]  Nicolas Papadakis,et al.  Variational Assimilation of Fluid Motion from Image Sequence , 2008, SIAM J. Imaging Sci..

[29]  Philippe Courtier,et al.  Sea surface velocities from sea surface temperature image sequences: 1. Method and validation using primitive equation model output , 2000 .

[30]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[31]  Jacques Froment,et al.  Reconstruction of Wavelet Coefficients Using Total Variation Minimization , 2002, SIAM J. Sci. Comput..

[32]  A. N. Tikhonov,et al.  The regularization of ill-posed problems , 1963 .

[33]  T. Corpetti,et al.  Pressure image assimilation for atmospheric motion estimation , 2009 .

[34]  J. Schmetz,et al.  Operational Cloud-Motion Winds from Meteosat Infrared Images , 1993 .

[35]  Isabelle Herlin,et al.  Estimation of a Motion Field on Satellite Images from a Simplified Ocean Circulation Model , 2006, 2006 International Conference on Image Processing.

[36]  A. Piacentini,et al.  Variational data analysis with control of the forecast bias , 2004 .

[37]  C. W. Groetsch,et al.  Regularization of Ill-Posed Problems. , 1978 .

[38]  Anestis Antoniadis,et al.  Wavelet methods in statistics: Some recent developments and their applications , 2007, 0712.0283.