13,697 research outputs found
Solving ill-posed Image Processing problems using Data Assimilation
International audienceData Assimilation is a mathematical framework used in environmental sciences to improve forecasts performed by meteorological, oceanographic or air quality simulation models. It aims to solve an evolution equation, describing the temporal dynamics, and an observation equation, linking the state vector and observations. In this article we use this framework to study a class of ill-posed Image Processing problems, usually solved by spatial and temporal regularization techniques. An approach is proposed to convert an ill-posed Image Processing problem in terms of a data Assimilation system, solved by a 4D-Var method. This is illustrated by the estimation of optical ow from a noisy image sequence, with the dynamic model ensuring the temporal regularity of the result. The innovation of the paper concerns first, the extensive description of the tasks to be achieved for going from an image processing problem to a data assimilation description; second, the theoretical analysis of the covariance matrices involved in the algorithm; and third a specic discretisation scheme ensuring the stability of computation for the application on optical flow estimation
Recommended from our members
On sequential multiscale inversion and data assimilation
Multiscale approaches are very popular for example for solving partial differential equations and in many applied fields dealing with phenomena which take place on different levels of detail. The broad idea of a multiscale approach is to decompose your problem into different scales or levels and to use these decompositions either for constructing appropriate approximations or to solve smaller problems on each of these levels, leading to increased stability or increased efficiency. The idea of sequential multiscale is to first solve the problem in a large-scale subspace and then successively move to finer scale spaces.
Our goal is to analyse the sequential multiscale approach applied to an inversion or state estimation problem. We work in a generic setup given by a Hilbert space environment. We work out the analysis both for an unregularized and a regularized sequential multiscale inversion. In general the sequential multiscale approach is not equivalent to a full solution, but we show that under appropriate assumptions we obtain convergence of an iterative sequential multiscale version of the method. For the regularized case we develop a strategy to appropriately adapt the regularization when an iterative approach is taken.
We demonstrate the validity of the iterative sequential multiscale approach by testing the method on an integral equation as it appears for atmospheric temperature retrieval from infrared satellite radiances
Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation
Improved estimation of hydrometeorological states from down-sampled
observations and background model forecasts in a noisy environment, has been a
subject of growing research in the past decades. Here, we introduce a unified
framework that ties together the problems of downscaling, data fusion and data
assimilation as ill-posed inverse problems. This framework seeks solutions
beyond the classic least squares estimation paradigms by imposing proper
regularization, which are constraints consistent with the degree of smoothness
and probabilistic structure of the underlying state. We review relevant
regularization methods in derivative space and extend classic formulations of
the aforementioned problems with particular emphasis on hydrologic and
atmospheric applications. Informed by the statistical characteristics of the
state variable of interest, the central results of the paper suggest that
proper regularization can lead to a more accurate and stable recovery of the
true state and hence more skillful forecasts. In particular, using the Tikhonov
and Huber regularization in the derivative space, the promise of the proposed
framework is demonstrated in static downscaling and fusion of synthetic
multi-sensor precipitation data, while a data assimilation numerical experiment
is presented using the heat equation in a variational setting
Variational Data Assimilation via Sparse Regularization
This paper studies the role of sparse regularization in a properly chosen
basis for variational data assimilation (VDA) problems. Specifically, it
focuses on data assimilation of noisy and down-sampled observations while the
state variable of interest exhibits sparsity in the real or transformed domain.
We show that in the presence of sparsity, the -norm regularization
produces more accurate and stable solutions than the classic data assimilation
methods. To motivate further developments of the proposed methodology,
assimilation experiments are conducted in the wavelet and spectral domain using
the linear advection-diffusion equation
Solving Ill-posed Problems Using Data Assimilation. Application to optical flow estimation
ISBN 978-989-8111-69-2International audienceData Assimilation is a mathematical framework used in environmental sciences to improve forecasts performed by meteorological, oceanographic or air quality simulation models. Data Assimilation techniques require the resolution of a system with three components: one describing the temporal evolution of a state vector, one coupling the observations and the state vector, and one defining the initial condition. In this article, we use this framework to study a class of ill-posed Image Processing problems, usually solved by spatial and temporal regularization techniques. A generic approach is defined to convert an ill-posed Image Processing problem in terms of a Data Assimilation system. This method is illustrated on the determination of optical flow from a sequence of images. The resulting software has two advantages: a quality criterion on input data is used for weighting their contribution in the computation of the solution and a dynamic model is proposed to ensure a significant temporal regularity on the solution
- …