Image processing and physical models

Problematic: This is one of the innovative direction of this proposal. The challenge is to incorporate within image processing methods all the available information, concerning the observed phenomenon (cloud, land use, ...), the data acquisition process (radiative transfer, physical models of the atmosphere, ...) and to establish regularity constraints that account for the image nature of data.

Objectives: Studies are done on inverse problems formulation for the computation of cloud parameters. Focus is made on temporal conservation hypothesis and their formulation. Equations are based on simplified modelling of the atmosphere and radiative transfer, using regularization models.

We identify the following scientific objectives:

• the type of regularization must be reconsidered: use a Tykhonov regularizer for example, better adapted to the nature of data, or introduce other regularization operators that take into account the physical nature of data or phenomenon.
• Reconsider the physical model of image information (and consequently the radiative transfer model and the atmospheric model) with different characteristics (2D, 3D or 4D, gaseous or multiphasic chemistry) according to the needs of the different applications. We also need the gradient of these various model levels w.r.t. their parameters (these gradients are obtained by derivation for simple models or with automatic differentiation code in the case of more complex models). These models, associated with their gradients, must be coupled with chemistry transport code (developed by CEREA) for satellite data assimilation.
• In such a context, parameter estimation must be revisited, all the more because research performed in remote sensing (next subsection) produce information necessary for their validation. Parameter estimation typically necessitates the inversion of a model that explains the image data. In the context of pre-operational studies, these models are simplified representations of physical processes, sometimes they are only statistical. They are inverted pixel per pixel, independently. When atmospheric or radiative transfer models are at hand, the goal is to perform inversion of these models to obtain atmospheric parameters, for examples those parameters related to cloud cover. The main difficulty comes from the fact that radiative transfer model inversion is highly ill-posed : no unique solution, instability. In our approach, we want to set up the inversion process while considering the image nature of data. In that respect, our goal is to derive spatial regularization constraints needed for this model inversion.
• It is a fundamental point, in the domain of satellite data, to reexamine motion models: one can for instance use fluid mechanics, and take into account Navier-Stokes equations and advection-diffusion models, instead of the ad-hoc (affine) models that are usually considered in image processing.